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1. Elements of the Theory of Functions
2. Introductory Functional Analysis
3. Functional Analysis (Pure and
4. Functional Data Analysis with
5. Functional Analysis
6. Functional Analysis of Problem
7. Applied Functional Analysis
8. A Course in Functional Analysis
9. The Functional Analysis of English:
10. Functional Analysis and Linear
11. Elementary Real and Complex Analysis
12. Theoretical Numerical Analysis:
13. Real and Functional Analysis (Graduate
14. Functional Analysis
15. Gian-Carlo Rota on Analysis, Convexity,
16. Analysis II: Differential and
17. Functional Analysis, Sobolev Spaces
18. Elementary Functional Analysis
19. A First Course in Functional Analysis
20. Functional Analysis

1. Elements of the Theory of Functions and Functional Analysis
by A. N. Kolmogorov, S. V. Fomin
 Paperback: 288 Pages (1999-02-16)
list price: US$15.95 -- used & new: US$8.99
(price subject to change: see help)
Asin: 0486406830
Average Customer Review: 4.5 out of 5 stars
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Based on the authors’ courses and lectures, this two-volume advanced-level text is now available in a single volume. Topics include metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque interval, Hilbert Space and more. Each section contains exercises. Lists of symbols, definitions and theorems. 1957 ed.
... Read more

Customer Reviews (14)

1-0 out of 5 stars Poor notation
Don't buy this book! Although this book is cheap, the quality is nowhere up to the standard you would be expecting. The book's notation is utterly hard to read and understood. It is too compact that the proofs are harder than anything to follow.

5-0 out of 5 stars Can't get any better than this
There are 2 parts in this book. Matrix spaces etc are discussed in one and the second part covers topics like Lebesgue integration. After looking through some other text books, I have to say that this is probably the best book I read. I finally understand the topic very well. Also another important thing I like is the way proofs are written. If you have a class to follow, then this book is the perfect combination. If you have read the basics elsewhere that can also help. But overall it is very well written

5-0 out of 5 stars Excellent book, good price
A concise, well-readable book for as much money as every textbook should cost. There's only one problem I found, but I wouldn't take a star for it, because the book is really very good: since the book is quite old, the nomenclature is very different from the current one. (Eg. the empty set is called ``void set'', Cauchy sequences is called ``fundamental sequences'', etc.) One should always look up the ``up-to-date'' name of every important concept that is introduced in the book.

5-0 out of 5 stars Better than his fabulous Real Analysis book
This book is better than his fabulous Real Analysis book. It is one of the best, if not THE best, functional analysis book out there and the price is low. Quality to price ratio is approaching infinity here (as Dover reduces the price more)!!!

Kolmogorov knows how to arrange topics and introduce them at the proper spots throughout the book.Everything is broken down into bite sized pieces and you are given enough examples to digest what's going on.Reading the book is like reading Kolmogorov's mind, as he has tried to teach HOW TO THINK about the material, not just DO IT. It's also very addictive, even though it's rigorous.

Name a better functional analysis book?Not sure if that's possible.

5-0 out of 5 stars It's a classic
I own the book in Spanish language. Some content in the book is not easy stuff, if you study by others books, but Kolmogorov has the gift to make easy things that aren't quite so easy. Perhaps some theory is "old", because all the new books use some diferent approach to the subject, like the chapter dedicated to the Lebesgue integral, the book give the definition of a simple function in a different manner that we use today. The book is a must to have in your library, when you need to work with Functional Analysis. ... Read more

2. Introductory Functional Analysis with Applications
by Erwin Kreyszig
Paperback: 704 Pages (1989-02-23)
-- used & new: US$72.29
(price subject to change: see help)
Asin: 0471504599
Average Customer Review: 5.0 out of 5 stars
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Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis. ... Read more

Customer Reviews (18)

5-0 out of 5 stars Excellent Text - I refer to it now and again
This is one text that I refer to every now and again. This text was my coursework book when I did my functional analysis at for my honours module at University of South Africa. I am now a graduate student doing MSc. Even though I am now reading from advanced texts in operator algebras, I refer to Kreyzig for explicit explanations.My hat goes off to Prof. Kreyzig.Excellent text.

5-0 out of 5 stars Classic book on the subject
Best introductory book to study the subject. It is adopted as the textbook in my university, on a post-grad discipline. Professor Kreyszig was very successful when he decided to write about that interesting subject for teaching students of engineering and of Mathematics. I am very glad to have bought this book. LAN

5-0 out of 5 stars I join the rest of the reviewers - magnificent
I have taken a look at the other reviews and all of them agree that this is an amazingly well written book. Only a couple of proofs are missing, so the whole book is mostly self-contained. There is almost no balance between understandability and academic rigor, and the book makes as good a read as a novel. The pre-requisites, giventhe advanced topic (at least for non mathematicians like me) are minimal. I plan on reading even the parts I don't immediately need for my work.
If you want to read functional analysis as fast as you can read a mainstream piece of literature, get this book, it's worth every penny.

5-0 out of 5 stars My favorite math book
This book is an exceptionally well written book. It assumes very little previous knowledge, and develops the subjects clearly, with understanding in mind (as opposed of just being 'correct'). The author motivates the material, explains it and then proves it.
I fell in love with Hilbert Spaces reading this book. It balances the abstract nature of the subject with "applications". The problems are insightfull and a pleasure to solve.

5-0 out of 5 stars Two thumbs up!
I dont have a lot to say, but ijust wanted to say that this book is really written for the student, without any complications a student can alone read it and understand it,,, ... Read more

3. Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
by Peter D. Lax
Hardcover: 608 Pages (2002-04-04)
list price: US$125.00 -- used & new: US$70.90
(price subject to change: see help)
Asin: 0471556041
Average Customer Review: 4.5 out of 5 stars
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Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.
* Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.
* Includes an appendix on the Riesz representation theorem. ... Read more

Customer Reviews (7)

5-0 out of 5 stars Magic of the classroom
Peter Lax leaves the magic of the mathematics, and his understanding thereof, in plain view. The author preserves in his written wordsthe enthusiasm for mathematics that he has in the classroom.The book though permits the reader to proceed as his time permits as the results are set out in a number of brief chapters each of which has something of significance for the reader. This book should be of interest even to the expert who knows the results but who likes to read carefully crafted prose and who would like to understand some of the author's views about the way to think about mathematics.It is well worth the effort.

5-0 out of 5 stars By far the best book on the subject out there
The book makes the subject fun while covering a lot of material. The author is an excellent mathematician, and this shows through on every page. The historical asides are very informative (if depressing, since they all, by choice, since Lax writes about the generation which influenced him (and a lot of which perished in the concentration camps, a fate Lax narrowly escaped himself, as did another giant of functional analysis (of a rather different style) -- A. Grothendieck)

5-0 out of 5 stars Great book, for its target audience.
This is a very good book, provided you belong to its target audience. Ideally, this means you are a grad student in math or applied math, with at least some basic knowledge in FA. I would not recommend it as a first book on the topic for someone who has never seen FA. But if you did pick up some FA along the way and now you want to take a step to the next level - this book would be a great choice.

The author also supplies important historical facts about how many of the great mathematicians in the field of FA were murdered by the Nazis (most, but not all, of them were Jewish). Now forget the math for a second; for this alone, the book is important.

1-0 out of 5 stars typical expensive and unenlightening math text
This text is more suited as a review for someone
who already knows the results.There is very
little in the way of motivation for the various

5-0 out of 5 stars Functional analysis
This is a very elegant text. The analysis theorems and proofs are well explained and connected with operator theory. The exercises are well chosen to further the reader's understanding of the subject.
I strongly recommend this book both as a class text and as a refence volume. ... Read more

4. Functional Data Analysis with R and MATLAB (Use R)
by James Ramsay, Giles Hooker, Spencer Graves
Paperback: 202 Pages (2009-07-01)
list price: US$59.95 -- used & new: US$28.07
(price subject to change: see help)
Asin: 0387981845
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Scientists often collect samples of curves and other functional observations, and develop models where parameters are also functions. This volume in the UseR! Series is aimed at a wide range of readers, and especially those who would like apply these techniques to their research problems. It complements Functional Data Analysis, Second Edition and Applied Functional Data Analysis: Methods and Case Studies by providing computer code in both the R and Matlab languages for a set of data analyses that showcase functional data analysis techniques. The authors make it easy to get up and running in new applications by adapting the code for the examples, and by being able to access the details of key functions within these pages. This book is accompanied by additional web-based support at http://www.functionaldata.org for applying existing functions and developing new ones in either language. The companion 'fda' package for R includes script files to reproduce nearly all the examples in the book including all but one of the 76 figures.

... Read more

5. Functional Analysis
by Walter Rudin
Hardcover: 448 Pages (1991-01-01)
-- used & new: US$60.00
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Asin: 0070542368
Average Customer Review: 4.5 out of 5 stars
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This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem. ... Read more

Customer Reviews (6)

4-0 out of 5 stars Functional Analysis (McGraw-Hill Series in Higher Mathematics)
Basically this book is legible, but there are some ruins on the cover and it is the first edition not the second edition.

3-0 out of 5 stars As a reference, this is nice, but as a book for first-time learners...
I enjoy perusing Rudin's "Functional Analysis" at this stage in my life. It is fairly nice tome for functional analysis, and its general treatment of topological vector spaces (as opposed to the standard Banach space examples studied in a typical functional analysis class) is now well-received.

However, as a student, I was put off by this book. At times, I found it difficult to tie the theory present to the basic examples which were relevant at the time (such as L^{p} spaces). For a first time learner, I would suggest the book of Kolmogorov and Fomin (which is a Dover book, by the way), and would wait until later for this book.

5-0 out of 5 stars Outstanding
Hardly can I find words to highlight the goodness of this book. As mentioned by other readers ,it provides elegant, direct and powerfool proofs of the three theorems which constitute the cornserstones of functional analysis (Hanh-Banach, Banach-Steinhaus and Open mapping). These theorems are, in addition, studied in their most general context, namely topological vector spaces.

Specially appealing is its treatment of distributions' theory. It is, as far as I know, the only text which start by defining the rigurous topology on the set of test functions and then obtains the convergence and continuity of functionals (distributions) in terms of this topolgy, which is, indeed, the only way to present and gain insight into these concepts and to reach some results such as completness. In doing otherwise one riskdefinitions can emerge as artificial and rather arbitrary.

It is, without any doubt, a must have book for those with interest in pure mathematics as well as for those who, eventually, realize that the only way to dominate their area is saling through mathematics.

5-0 out of 5 stars Modern topics in math.
"Modern analysis" used to be a popular name for the subject of this lovely book. It is as important as ever, but perhaps less "modern". The subject of functional analysis, while fundamental and central in the landscape of mathematics, really started with seminal theorems due to Banach, Hilbert, von Neumann, Herglotz, Hausdorff, Friedrichs, Steinhouse,...and many other of, the perhaps less well known, founding fathers, in Central Europe (at the time), in the period between the two World Wars. In the beginning it generated awe in its ability
to provide elegant proofs of classical theorems that otherwise were thought to be both technical and difficult. The beautiful idea that makes it all clear as daylight: Wiener's theorem on absolutely convergent(AC) Fourier series of 1/f if you can divide, and if f has the AC Fourier series, is a case in point. The new subject gained from there because of its many sucess stories,- in proving new theorems, in unifying old ones, in offering a framework for quantum theory, for dynamical systems, and for partial differential equations. And offering a language that facilitated interdisiplinary work in science! The Journal of Functional Analysis, starting in the 1960ties, broadened the subject, reaching almost all branches of science, and finding functional analytic flavor in theories surprisingly far from the original roots of the subject. The topics in Rudin's book are inspired by harmonic analysis. The later part offers one of the most elegant compact treatment of the theory of operators in Hilbert space, I can think of. Its approach to unbounded operators is lovely.

5-0 out of 5 stars The Bible on Distributions
No other book covers the elements of distributions and the fourier transform quite like Rudin's Functional Analysis.This is a must for every budding PDE-er! ... Read more

6. Functional Analysis of Problem Behavior: From Effective Assessment to Effective Support (The Wadsworth Special Educator Series)
by Alan C. Repp, Robert H. Horner
Paperback: 432 Pages (1999-02-01)
list price: US$168.95 -- used & new: US$119.20
(price subject to change: see help)
Asin: 0534348505
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Contains several articles by experts in the fields of special education and psychology. Each article explores the issues, theories, and practices of assessing problem behavior and determining how to use this information. Together, the articles of this text present current advances in the use of functional assessment technology: taking the techniques and strategies of traditional functional analysis and using this information to construct clinical interventions. Three sections focus on the following topics: how functional assessment can be used to intervene effectively and change problem behavior, common procedures for using functional assessment in the preschool and school classroom, and new directions and trends in the field of functional assessment. A thorough and well-researched base of knowledge on problem behavior is provided, and the student learns the many ways in which this behavior may be diagnosed, intervened, and ideally changed. ... Read more

7. Applied Functional Analysis
by D.H. Griffel
Paperback: 390 Pages (2002-06-14)
list price: US$22.95 -- used & new: US$12.90
(price subject to change: see help)
Asin: 0486422585
Average Customer Review: 4.5 out of 5 stars
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A stimulating introductory text, this volume examines many important applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Detailed enough to impart a thorough understanding, the text is also sufficiently straightforward for those unfamiliar with abstract analysis. Its four-part treatment begins with distribution theory and discussions of Green's functions. Essentially independent of the preceding material, the second and third parts deal with Banach spaces, Hilbert space, spectral theory, and variational techniques.The final part outlines the ideas behind Frechet calculus, stability and bifurcation theory, and Sobolev spaces. 1985 ed. 25 Figures. 9 Appendices. Supplementary Problems. Indexes.
... Read more

Customer Reviews (8)

3-0 out of 5 stars Meh...
I don't know what all these people are trying to do by saying that this book is "the best book on functional analysis". It's not. I think if one is looking for a "Functional Analysis-Lite" kind of book, you could do better. If you want to learn about Banach and Hilbert spaces, other books would be more thorough and helpful, especially for physicists learning about it grad school having to grapple with it all the time.

The book is divided into 4 parts, and I will discuss each part.

I. Distribution Theory and Green's Functions
II. Banach Spaces and Fixed Point Theorems
III. Operators in Hilbert Spaces
IV. Further Developments

PART I: This is actually a bit more confusing and unclear than it needs to be. A lot of it could be done with more motivation. The actual chapter on Green's functions and PDEs is pretty standard, more or less. I've seen Green's functions discussed better in books by Partial Differential Equations of Mathematical Physics and Integral Equations and also in Methods of Theoretical Physics, Part I. For PDEs and Green's functions solutions, I would recommend a book devoted to PDEs that also covers Fourier Transform methods - there are plenty.

Part II: The chapter on Normed Spaces is not too bad. The discussion is helpful. It helps one understand only the very basics. If you are an applied mathematician developing theories for numerics, or trying to solve intricate PDE problems, I recommend looking at the first half of Elements of the Theory of Functions and Functional Analysis and especially Introductory Functional Analysis with Applications. Their discussion of the fixed point theorems and the Contraction Mapping Theorem (of which Newton's method of solving for zeros is an example), IMHO, are far superior and enlightening. The two just mentioned actually teach you how to think as a mathematician, relatively painlessly. The only advantage is that Griffel's book touches on some modern applications which you may or may not encounter.

Part III: This portion is like a physicists introduction to Hilbert spaces and applications. Here the last book mentioned does a superb job at introducing the material - both Hilbert spaces and Operator theory. In fact, there is also a chapter on on unbounded operators in quantum mechanics in the Kreyszig book that I noticed is missing in Griffel's. The advantage of Griffel's book is that there is a pretty good discussion of Variational methods that I've only seen elsewhere in Linear Algebra and PDE books.

Part IV: I actually cannot comment on this because I did not go too deeply into this material. For Sobolev spaces I looked elsewhere. I never needed the Frechet derivative. Other reviews seem to like it, though.

I have heard some of my students use this book for a class (not taught by me). They were thoroughly confused when going over the material in part I. They did not have knowledge of Real Analysis coming in. For students and classes with students like these, I recommend Introductory Functional Analysis with Applications. For students with little to no prior experience with Real Analysis, I recommend Elements of the Theory of Functions and Functional Analysis. For students with experience in Real Analysis, I recommend the last book mentioned, or one of my favorites, Elementary Functional Analysis. This last book covers a lot of the material that Griffel does (not all); it goes deeper into issues regarding normed vector spaces, Hilbert spaces, etc... ; it teaches one to think like a mathematician (applied or otherwise) and is useful, in my opinion, for physicists as well.

I am not an analyst, I taught myself a lot of this material and Griffel was not helpful when I was taking courses that covered the same stuff and when I was trying to learn about functional analysis. I offer the above list of books as alternatives to finding good stuff - I'm sure other resources exist.

5-0 out of 5 stars An excellent book on functional analysis
For some time I was trying to find a book on functional analysis that wasn't too technical nor too elementary. Even though there are excellent books on this domain none of them suited me. Griffel's book is exactly what I needed. Well structured, with a lot of examples and an effort to communicate the ideas behind the technicalities, makes the study and understanding of the domain fluent.

3-0 out of 5 stars Just didn't grab me
The book is a little short on rigor sometimes, which is usually not a big deal for non-mathematicians.However, my main complaint is the author's writing style, somehow i could not sit down and read this book (a problem i usually don't have, even with books on things like functional analysis).I can't really put my finger on what it was, but he just didn't make the subject interesting for me. That being said, there's a lot of good stuff in here, and it has the added bonus of costing less than $15.

5-0 out of 5 stars The BEST book there is in introductory Functional Analysis
This is the best book in Introductory functional Analysis book I know and I know a lot of them. Why is it so good? Thedefinitions are very well motivated. Then the subtle points are illustrated with examples.Then there are the theorems all well motivated and with simple ,very well explained proofs. Then there are the applications to engineering and physics .All the aplications are well explained. There is no danger of not understanding the application. Then there are the problems with notes on them at the end ( The author offers you the complete solutions for a pittance)Finally the price....You can not beat this book

4-0 out of 5 stars Written for engineers and applied mathematicians
I was not looking for rigorous definitions. This book explains concepts clearly without oversimplifying. ... Read more

8. A Course in Functional Analysis (Graduate Texts in Mathematics)
by John B. Conway
Paperback: 420 Pages (2010-11-02)
list price: US$79.95 -- used & new: US$64.09
(price subject to change: see help)
Asin: 1441930922
Average Customer Review: 4.0 out of 5 stars
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This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general.

From the reviews: "This book is an excellent text for a first graduate course in functional analysis....Many interesting and important applications are included....It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author." --MATHEMATICAL REVIEWS

... Read more

Customer Reviews (4)

3-0 out of 5 stars For Pure Math Courses Only
This book is appropriate for a graduate course in functional analysis in a mathematics department. It assumes a strong background in undergraduate topology, advanced linear algebra (a linear algebra course that covered direct sums and products, dual spaces, quotient spaces, isomorphisms, and universal mapping properties) and complex analysis, along with a graduate level course in real analysis and measure theory. This book should not be used for a graduate course in Applied Functional Analysis (as it was when I took it). Very few applications are discussed, there is only one diagram in the entire book, proofs skip many intermediate steps, and examples are stated with no explanation. If you do not have the equivalent knowledge of a bachelors in pure mathematics, this book will be almost unreadable. The take home message here is that this book is not for quantitative scientists (who use a lot of functional analysis tools without even knowing it) to study the basic theory behind the tools they use. Its designed for exactly what it says, "a graduate course in mathematics". So if you are a Professor about to teach a course in "Applied Functional Analysis" do not use this book. Use one of the many books called Applied functional analysis.

That being said, I did appreciate the order of coverage. Starting with Hilbert spaces and then moving to Banach spaces, made things more clear for me.

4-0 out of 5 stars A wonderful first course for enthousiasts
The only reason for 4 stars instead of 5 is that I am not a great fan of Conway's style, and have wasted too much time on mangled examples in his Complex Analysis.
That said, the layout here is superb, and the choice of topics just what is needed to get one of the ground. Beginners will find it useful to have a copy of Kreyszig at hand.

5-0 out of 5 stars A Course in Functional Analysis ... the title is correct!
I learned functional analysis by studying this book. I did this under the direction of a master teacher, John Erdman, who taught via a modified Moore Method. I found this very inspirational and challenging. BEFORE I took thecourse, I did not enjoy browsing the book, BUT I learned that the book,upon combination with the right amount of focus and effort, did aremarkable job of bringing functional analysis alive ... of transmiting thereal essence to young, "sprouting" mathematicians. There is alsoan informality that brings a freshness to the book ... and this in asubject that could easily be studied without encountering this importantingredient in a mathematician's training.

This book has as it's highpoint and goal the spectral theorem for normal operators. I add thisbecause no one book can be all encompassing. If this and the spectraltheorem goal are kept in mind, the omissions and emphasis found in the bookwill be found to be completely natural.

This book should be in thelibrary of anyone teaching functional analysis or who wants a workingmathematician's masterfully developed course on functional analysis (withan eye to the spectral theorem for normal operators).

5-0 out of 5 stars An Excellent Book !
This book is just excellent. The author decides to do something a little unusual, and starts talking about "Hilbert Spaces" before talking about "Banach Spaces". Conway writes down the matereal in a greatway. He gives proves to almost every proposition, and gives lots ofEXAMPLES and EXCERCISES (which are not given in most of the books aboutthis subject). It's a good book for people who have never read this bookbefore, as well as people who are currently studying the course. Also,conway extends the book's content by writing about advanced subjects (thatare not studied in a first course about the subject), like locally convexspaces, weak topologies and even unbounded operators. ... Read more

9. The Functional Analysis of English: A Hallidayan Approach (Arnold Publication)
by Thomas Bloor, Meriel Bloor
Paperback: 332 Pages (2004-09-23)
list price: US$45.00 -- used & new: US$31.57
(price subject to change: see help)
Asin: 034080680X
Average Customer Review: 3.5 out of 5 stars
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This book presents the principles of a Hallidayan approach to language studies, and introduces a set of techniques for the grammatical analysis of English. It includes an overview of the applications of functional grammar that demonstrates the practical importance of linguistic theory and analysis in relation to issues in education and society. This edition also locates Michael Halliday and his school within the history of linguistics. Linguistic terms are clearly explained and illustrated with authentic examples from a wide variety of sources including scientific and technical texts. ... Read more

Customer Reviews (2)

2-0 out of 5 stars None the wiser for reading this book
I thought this book would allow me to understand functional grammar.

Instead, I found a book that sets out a particular analysis without adequately explaining why such an analysis has been arrived at. It is the worst kind of 'school textbook', telling the student what the dogma is without trying to reason with him/her, as a presumably intelligent person, why such an analysis is the preferred one.

For instance, their analysis of 'The kettle is boiling' into Given information ('the kettle') and New Information ('is boiling') makes no sense to me at all. All that this analysis does is take the underlying Subject/Predicate construction and reinterpret it as Given/New. In fact, my intuition is that 'The kettle is boiling' forms a single unit in which the WHOLE SENTENCE is New information.

Because the book does not try to discuss with the reader why this analysis has been adopted, it is impossible to figure out what the principles of analysis should be. From reading this book, I still don't have a clear idea how functional grammar analyses sentences.

I would not recommend this book.

5-0 out of 5 stars An excellent introduction to functional grammar
Halliday's functional grammar is a unique way of describing how language is actually used in a social situation.This is not a grammar of rules, but rather an analysis of language and its functions.

Tom and MerielBloor's book is the best introduction to this grammar.Written as a coursetextbook, with a clear, methodical presentation and exercises, it can alsobe read as a general introduction for the curious.It is complete andhighly readable, and the grammatical theories it presents and explains canbe useful to anyone who works with language, to better understand howlanguage works.Language is not examined here out of context - in fact,context is one of the key factors in Halliday's grammar - rather, Bloor andBloor show how isolated bits of text fit in with the larger perspective oflanguage as a whole. ... Read more

10. Functional Analysis and Linear Control Theory (Dover Books on Engineering)
by J. R. Leigh
Paperback: 176 Pages (2007-03-16)
list price: US$11.95 -- used & new: US$2.48
(price subject to change: see help)
Asin: 048645813X
Average Customer Review: 3.5 out of 5 stars
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Functional analysis provides a concise conceptual framework for linear control theory. This self-contained text, geared toward engineering students, demonstrates the subject's unity. A wide range of powerful theorems illustrates inner product spaces; instability, controllability, and observability; minimum norm and time control; and distributed systems. 1980 edition.
... Read more

Customer Reviews (2)

4-0 out of 5 stars a concise mathematical state space control book
This short book presents an overview of mathematical results (i.e. proofs) concerning existence and uniqueness for linear state space methods of control theory. A good prerequisite would be that you already know either some functional analysis or some state space control theory, and you want to see how these two fields work together. The author covers topological, Banach, and Hilbert spaces and their applicability to optimal controllers via typical control theory cost functions. Some material on distributed systems is presented at the end. The few worked examples are trivial in nature compared to typical control theory books, but this is in keeping with the abstract mathematical nature of the book. Since this book is a 1980 edition, many addition interesting results are presumably known today (2008), but this book seems to be a good starting point. For a less proof oriented book, still done with somewhat of a mathematical bent and with many more examples, consider the masterpiece, Modern Control Theory, by Brogan. Happy controlling.

3-0 out of 5 stars Thin and non-uniform
A very thin book that suffers from a nonuniform level of presentation.
Attempts to treat optimal control from a functional analytic viewpoint. You
have to basically know functional analysis very well as a prerequisite.
There is a nice editorialized bibliography in each chapter. ... Read more

11. Elementary Real and Complex Analysis (Dover Books on Mathematics)
by Georgi E. Shilov
Paperback: 528 Pages (1996-02-07)
list price: US$19.95 -- used & new: US$11.75
(price subject to change: see help)
Asin: 0486689220
Average Customer Review: 4.5 out of 5 stars
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Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, series, the derivative, higher derivatives, the integral and more. Each chapter contains a problem set (hints and answers at the end), while a wealth of examples and applications are found throughout the text. Over 340 theorems fully proved. 1973 edition.
... Read more

Customer Reviews (9)

3-0 out of 5 stars The price is right...
Can't beat the price, and the material is well-presented and organized, but it's stripped down to the bare essentials - theorem, proof, lemma, corollary, etc. It's not a book on proof methodology, for sure. I graduated with a degree in computer science, but I haven't done a proof for a while and never took a class beyond linear algebra, and I wanted to teach myself analysis. While I don't find the material too difficult to follow, I really don't find it all that great for self-study. The book yields conclusion after conclusion, but among all the results, I find the text doesn't do a great job of conveying its methodology. In other words, the book spends the vast majority of the time developing new results (the "what" of analysis), but it does little to prepare the reader to understand the "how" of analysis. I feel as though the book is giving me a fish, rather than teaching me to fish.

And there are some idiosyncracies. You need to be wary of an occasionally swapped subscript, for instance. And in chapter 1 problem 5: Which is larger, Sqrt(3) + Sqrt(5) or Sqrt(2) + Sqrt(6)? The answer in the back of the book is plain wrong. And the book proves something as fundamental as the uniqueness of 1; and yet it invokes the binomial theorem out of the blue?

Anyway, the price is right, but beware that it might make a better reference or a collection of examples than a primary self-study guide.It's not that it's "too easy" as one reader put it; rather, it doesn't integrate the material with exercises and explanations well enough for my liking.

5-0 out of 5 stars It is one very interesting book
To me, the best chapters of this book are that about series and integrals. The text is plenty of interesting notions, like that of direction that is related with the notion of limit. I appreciated very much the study that Shilov does about parameter-dependent proper and improper integrals. The topologicalnotions are placed in one intuitive manner. Without doubt, this is one very good and clear exposition about the subject. However, I think that the problems are not easy. Also sometimes Shilov states the theorems with additional conditions that are not useful. For example, this happens usually in the chapter about derivatives because the definition of derivative given by Shilov imposes that any function with derivative in the interval of the domain has continuous derivative in the interior points of its domain. However, Shilov charges some theorems with the extra condition of continuous derivative.
When the Taylor's formula is presented in page 252 - Theorem 8.22, it is stated that the error of the approximation is computed in some interior point of the interval, what is not completely correct. For example, take the second degree Taylor's approximation around x = 0 of the function x raised to the third power, and you will see that in this case the error is computed on one extreme point of the interval.
Also the proof of the theorem 10.49b (page 415) has logical problems of the kind that may arise during the translation.
However, these remarks are small questions without consequences for the course of the exposition.

5-0 out of 5 stars An excellent pure maths text.
I purchased this book to study some complex analysis.Being a physicist I would like to brush up on this.The book was completely different to what I expected.

Some applications would have been nice, but this text is pure maths.The book is well written, easy to follow and concise.I ended up reading it and gained and appreciation for the thorough consideration of elementary real and complex numbers.

Shilov is thorough and avoids making leaps and assertions.This would make the book readable to lower undergraduates.However the significance of some things is not explained, or explained in a very dry manner so people might miss this.

I highly recommend this book if you are interested in real and complex analysis from a pure mathematics perspective.

5-0 out of 5 stars Getting started in math analysis
This book by Shilov covers the fundamentals in beginning analysis(both real and complex). It has in common with Walter Rudin's book (entitled 'Real and Complex Analysis') that it covers both real functions (integration theory and more), as well as Cauchy's theorems for analytic functions. Shilov's book is at an undergraduate level, and it can easily be used for self-study. The Dover edition is affordable. Rudin's book is for the beginning graduate level, and it is widely used in math departments around the world. Both books have stood the test of time.
Comparison of Shilov with Rudin: Rudin's 'Real and Complex' has become an institution, and I have to admit I have loved it since I was a student myself, but conventional wisdom will have it that Shilov is a lot gentler on students, and much easier to get started with: It stresses motivation a bit more, the exercises are easier (some of Rudin's exercises are notorious, but I find the challenge charming--not all of my students do though!), and finally Shilov gets to touch upon a few applications; fashionable these days. But that part easily gets dated. I will expect that beginning students will enjoy Shilov's book.
Personally, I find that with perseverance, students who keep at it with Rudin's book, will end up with a lot stronger foundation. They are more likely to have proofs in their blood. I guess Shilov can always serve as a leisurely supplementary reading to Rudin.
There will never be another book like Rudin's 'Real and Complex', just like there will never be another van Gogh. But the fact that we love van Gogh doesn't prevent us from enjoying other paintings.

3-0 out of 5 stars Possibly too simple
As Shilov write in the introduction "I have tried to accomodate the interests of larger population of those concerned with mathematics" and at that he seems to do. However, the book does require some mathematical background as he appears to omit defining a few things. I believe the book would be ideal for those who want a handy reference, or an easier book when struggling with an analysis course.

However, for the more mathematically inclined readers, the problems are often too easy, and many things are proved that could be better left as exercises. For a more difficult Analysis book, I would reccomend Rudin. ... Read more

12. Theoretical Numerical Analysis: A Functional Analysis Framework (Texts in Applied Mathematics)
by Kendall E. Atkinson, Weimin Han
Hardcover: 625 Pages (2009-06-02)
list price: US$79.95 -- used & new: US$55.99
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Asin: 1441904573
Average Customer Review: 5.0 out of 5 stars
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This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study.

 Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added.

Review of earlier edition:

"...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references."

R. Glowinski, SIAM Review, 2003

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Customer Reviews (1)

5-0 out of 5 stars About Theoretical Numerical Analysis <br />by Kendall E. Atkinson
The book presents an abstract point of view of Numerical Analysis (as one can immediatly see by the title!). It is written by a master in the topic, author of more than 70 publications at the higher levels, well known for his contributions in Integral and Partial Differential Equations.

If one is interested on the basic aspects of numerical analysis, I also suggest to consider his well known manual "Elementary Numerical Analysis".

The present book presents several aspects that are not covered by most of the manuals in Numerical Analysis and highly contributes to have a wider idea of convergence and stability of some well known methods. ... Read more

13. Real and Functional Analysis (Graduate Texts in Mathematics) (v. 142)
by Serge Lang
Hardcover: 600 Pages (1993-04-29)
list price: US$74.95 -- used & new: US$56.13
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Asin: 0387940014
Average Customer Review: 4.5 out of 5 stars
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This book is meant as a text for a first-year graduate course in analysis. In a sense, the subject matter covers the same topics as elementary calculus - linear algebra, differentiation, integration - but treated in a manner suitable for people who will be using it in further mathematical investigations. The book begins with point-set topology, essential for all analysis. The second part deals with the two basic spaces of analysis, Banach and Hilbert spaces. The book then turns to the subject of integration and measure. After a general introduction, it covers duality and representation theorems, some applications (such as Dirac sequences and Fourier transforms), integration and measures on locally compact spaces, the Riemann-Stjeltes integral, distributions, and integration on locally compact groups. Part four deals with differential calculus (with values in a Banach space). The next part deals with functional analysis. It includes several major spectral theorems of analysis, showing how one can extend to infinite dimensions certain results from finite-dimensional linear algebra; a discussion of compact and Fredholm operators; and spectral theorems for Hermitian operators. The final part, on global analysis, provides an introduction to differentiable manifolds. The text includes worked examples and numerous exercises, which should be viewed as an integral part of the book. The organization of the book avoids long chains of logical interdependence, so that chapters are as independent as possible. This allows a course using the book to omit material from some chapters without compromising the exposition of material from later chapters. ... Read more

Customer Reviews (3)

5-0 out of 5 stars One of a kind !
Up to my knowledge, this is the only book that constructs the Lebesgue integral for functions to a general Banach-space instead of the real numbers (thus saving us from the unnecessary and esthetically dissapointing construction through positive and negative functions).
I don't know how Lang does it, but eerytime you'll pick up one of his books, you'll marvel at the beauty of mathematics !

5-0 out of 5 stars Much better than Royden!
It drove me up the wall, in my first course on measure and integration, that integration was first done for positive functions, then for real functions by writing them as a difference of positive functions, then complex functions in terms of real and imaginary parts.Why couldn't you just integrate real-valued functions
intrinsically, without the silly decomposition into positive and negative parts?

After that course, I found Lang's book.What a blessing to see that you can just integrate in infinite-dimensional spaces right from the start.I can't understand why virtually all books on integration theory still succumb to the "positive functions first" approach.

4-0 out of 5 stars Overall, A Good Book
I've read several analysis books and this is one of the better ones that I have read.It covers a variety of interesting and useful topics and the exposition is clear. It's presentation is a bit more abstract than some others starting with some functional-analytic concepts before doing integration in that framework. However, if you want to study stochastic analysis, getting in this frame of mind will definitely help your understanding of stochastic integration. For a truly thorough understaning of the subject, I recommend purchasing this book as well as the somewhat easier "Lebesgue Integration on Euclidean Space" by Frank Jones - the two together cost about the same as Royden, Rudin, or the terrible book by Aliprantis. ... Read more

14. Functional Analysis
by George Bachman, Lawrence Narici
Paperback: 544 Pages (1998-01-29)
list price: US$24.95 -- used & new: US$14.02
(price subject to change: see help)
Asin: 0486402517
Average Customer Review: 4.5 out of 5 stars
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Excellent treatment of the subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed and metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach theorem and its consequences, spectral notions, square roots, a spectral decomposition theorem, and many other related subjects. Chapters conclude with exercises intended to test and reinforce reader’s understanding of text material. A glossary of definitions, detailed proofs of theorems, bibliography, and index of symbols round out this comprehensive text. 1966 ed.
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Customer Reviews (3)

5-0 out of 5 stars Bachman and Narici's Functional Analysis
I find Bachman and Narici's book to be an excellent introduction to functional analysis for students who have had a graduate level linear algebra course and some introduction to measure theory.I completed a course in real analysis last year, and I wish I had immediately begun using this book. It seems to me to be somewhat less difficult than the real analysis course, based on Rudin, while reinforcing and building on topics that were introduced in real analysis and other masters level courses. Bachman and Narici's book seems to me to be a bit easier to follow than other functional analysis books, and to bridge the gap between what I already know and more difficult treatments of functional analysis. The book is excellent for self-study and would probably also serve well for a course.

5-0 out of 5 stars Clear and organised presentation
This book is perhaps the most organized in this field. It is very well written, the presentation really helps build the concepts elegantly and methodically. It is a must have for any one who is interested in learning functional analysis. Some advanced users may find that the book builds a bit slow but it will really help for those who are new in the field.

4-0 out of 5 stars A very clear exposition of the subject
Excelent book for graduate level engeneering or science students interested in applied or pure advance mathematics.This book is suitable for advance senior undergraduate students as well ... Read more

15. Gian-Carlo Rota on Analysis, Convexity, and Probability
by Jean Dhombres
Hardcover: 400 Pages (2002-12-06)
list price: US$134.00 -- used & new: US$7.02
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Asin: 0817642757
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Gian-Carlo Rota was one of those rare mathematicians who made major contributions to several areas of mathematics. Presented in the first part of this volume are reprints of his papers in analysis, which were written at the beginning of his career. These papers on differential equations, operator theory, ergodic theory, and other subjects have a continuing and pervasive influence. Reprints of his papers on convexity and probability theory are presented in the second part of the work. These were written towards the end of his career and contain many ideas that have yet to be fully developed. Comprehensive commentaries are included in every chapter. These survey articles detail work inspired by Rota's papers and also include discussions of many unsolved problems.

As is customary with Rota's writings, the papers included in the volume---some published here for the first time---contain many fresh and unexpected ideas for further research. Thus, this volume will be of interest to both experts and beginners in the above-mentioned fields.

Contributors: J. Dhombres, P.L. Duren, W.N. Everitt, D.A. Klain, J.P.S. Kung, A. Ramsay, M.M. Rao, J. Rovnyak, H.H. Schaefer, B. Schultze, J.T. Schwartz, N. Starr, G. Strang, D.C. Torney, R. Zaharopol, A. Zettl, X.-D. Zhang ... Read more

16. Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions (Universitext) (Pt. 2)
by Roger Godement
Paperback: 448 Pages (2005-12-01)
list price: US$69.95 -- used & new: US$11.89
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Asin: 3540209212
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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

... Read more

17. Functional Analysis, Sobolev Spaces and Partial Differential Equations (Universitext)
by Haim Brezis
Paperback: 598 Pages (2010-11-01)
list price: US$84.95 -- used & new: US$53.95
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Asin: 0387709134
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This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

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18. Elementary Functional Analysis
by Georgi E. Shilov
Paperback: 352 Pages (1996-01-18)
list price: US$16.95 -- used & new: US$5.00
(price subject to change: see help)
Asin: 0486689239
Average Customer Review: 5.0 out of 5 stars
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Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms—including problems in the complex domain, especially involving the Laplace transform—and more. Each chapter includes a set of problems, with hints and answers. Bibliography. 1974 edition.
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Customer Reviews (4)

5-0 out of 5 stars A beginning course in functional analysis
Elementary Functional Analysis by Georgi E. Shilovis suitable for a beginning course in functional analysis and some of its applications, e.g., to Fourier series, to harmonic analysis, to partial differential equations (PDEs), to Sobolev spaces, and it is a good supplement and complement to two other popular books in the subject, one by Rudin, and another by Edwards.
Rudin's book is entitled "Functional Analysis" (not in the Dover series) and it is my favorite.Rudin's book is of newer vintage, and it goes more in depth, and includes new material on unbounded operators in Hilbert space. Edwards' book "Functional Analysis: Theory and Applications;" is in the Dover series, and it is twice as thick as Shilov's book.
Topics covered in Shilov: Function spaces, L^p-spaces, Hilbert spaces, and linear operators; the standard Banach, and Hahn-Banach theorems. It includes many exercises and examples. Well motivated with applications.
Book Comparison:
Shilov book is gentler on students, and it is probably easier to get started with: It stresses motivation a bit more, the exercises are easier, and finally Shilov includes a few applications; fashionable these days. And of course, the books in the Dover series are cheap in comparison. Review by Palle Jorgensen, August 2007.

5-0 out of 5 stars Excellent book
This book is well organized, concise, and easy to read. Overall a very good deal.

4-0 out of 5 stars The book is very good but it is not self contained
I enjoyed the last chapters of the book, that are relative to the applications: differential geometry, Fourier series, Fourier transform, differential equations.
Also I think that the study of the convergence of Fourier series partially based on the notion of delta-like sequences of functions is very interesting and possibly it enables some generalizations.
However the book is not self-contained because it does very much references to 'Linear Algebra' and 'Elementary Real and Complex Analysis' of the author.

5-0 out of 5 stars another great book from Shilov
This is volume 2 of Shilov's Moscow University course on MathematicalAnalysis. If you have read Shilov's first volume ("Elementary Real andComplex Analysis") or his volume on Linear Algebra, then you canexpect more of the same clear explanation and thoughtful organization ofmaterials.His proofs are designed to help the reader understand materialand provide deep insight into the mathematics involved. Highly recommendedfor those who want a consise -- but very thorough -- introduction to theorybehind differential equations and Fourier analysis. ... Read more

19. A First Course in Functional Analysis (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
by S. David Promislow
Hardcover: 308 Pages (2008-04-25)
list price: US$115.00 -- used & new: US$63.95
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Asin: 0470146192
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A concise introduction to the major concepts of functional analysis

Requiring only a preliminary knowledge of elementary linear algebra and real analysis, A First Course in Functional Analysis provides an introduction to the basic principles and practical applications of functional analysis. Key concepts are illustrated in a straightforward manner, which facilitates a complete and fundamental understanding of the topic.

This book is based on the author's own class-tested material and uses clear language to explain the major concepts of functional analysis, including Banach spaces, Hilbert spaces, topological vector spaces, as well as bounded linear functionals and operators. As opposed to simply presenting the proofs, the author outlines the logic behind the steps, demonstrates the development of arguments, and discusses how the concepts are connected to one another. Each chapter concludes with exercises ranging in difficulty, giving readers the opportunity to reinforce their comprehension of the discussed methods. An appendix provides a thorough introduction to measure and integration theory, and additional appendices address the background material on topics such as Zorn's lemma, the Stone-Weierstrass theorem, Tychonoff's theorem on product spaces, and the upper and lower limit points of sequences. References to various applications of functional analysis are also included throughout the book.

A First Course in Functional Analysis is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practitioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis. ... Read more

20. Functional Analysis
by Frigyes Riesz, Bela Sz.-Nagy
Paperback: 491 Pages (1990-06-01)
list price: US$21.95 -- used & new: US$11.25
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Asin: 0486662896
Average Customer Review: 4.5 out of 5 stars
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Classic exposition of modern theories of differentiation and integration and the principal problems and methods of handling integral equations and linear functionals and transformations. Topics include Lebesque and Stieltjes integrals, Hilbert and Banach spaces, self-adjunct transformations, spectral theories for linear transformations of general type, much more. Translated from 2nd French edition by Leo F. Boron. 1955 edition. Bibliography.
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Customer Reviews (2)

4-0 out of 5 stars The standard work, but there are better
This is the "standard" book on the subject. It is referenced everywhere. It has a lot in it. I have not read it cover to cover, just used it for reference, but if you are new to the subject I think Kolmogorov and Fomin looks beeter, and Shilov's books look better too.

5-0 out of 5 stars Very readable classic
This book is a bargain ... in these days of $100 paperbacks ! The foreign authors, who 1st published this in the early 50s, write in a very readable way as opposed to most US profs. The book starts with an example of a continuous function which is not differentiable and then proves Lebesgue's theorem which tells you when a function does have a derivative.The 2nd part of the book is about Integral equations which again starts with some examples of problems the early 19th century mathematicians solved. Particularly interesting to me was Fredholm's method which was to replace the integral with a series. The book covers all the topics you would expect in a very readable form. ... Read more

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