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21. Functional Analysis: An Introduction
22. The Statistical Analysis of Functional
23. Applied Functional Analysis: Applications
24. Functional Analysis
25. Functional Analysis in Clinical
26. Functional Analysis (Springer
27. Functional Data Analysis (Springer
28. Nonlinear Functional Analysis
29. Applied Functional Data Analysis
30. Introductory Real Analysis
31. S+Functional Data Analysis: User's
32. Beginning Functional Analysis
33. Linear Functional Analysis (Springer
34. Functional Analysis - Applications
35. Real Analysis (4th Edition)
36. Nonparametric Functional Data
37. Functional Analysis And Semi-Groups
38. Signs and Symptoms Analysis from
39. Elementary Functional Analysis
40. Applied Functional Analysis (Applications

21. Functional Analysis: An Introduction (Graduate Studies in Mathematics)
by Yuli Eidelman, Vitali Milman, Antonis Tsolomitis
Hardcover: 322 Pages (2004-11-23)
list price: US$58.00 -- used & new: US$57.42
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Asin: 0821836463
Average Customer Review: 4.0 out of 5 stars
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This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators.

The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.

The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Great Condition Poor Choice of Text
Delivered fine. Great condition and delivered well on time. Wish my professor wasn't using this text, however. Not the best handling of the material that I've seen so far. ... Read more

22. The Statistical Analysis of Functional MRI Data (Statistics for Biology and Health)
by Nicole Lazar
Paperback: 299 Pages (2010-11-02)
list price: US$97.00 -- used & new: US$77.53
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Asin: 1441926798
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This book is a primer on fMRI for statisticians interested in learning more about this fascinating subject and the many statistical challenges inherent in functional neuroimaging data, laying out the basics of technique, and surveying the most popular current statistical approaches. ... Read more

23. Applied Functional Analysis: Applications to Mathematical Physics (Applied Mathematical Sciences) (v. 108)
by Eberhard Zeidler
Hardcover: 516 Pages (1995-06-23)
list price: US$134.00 -- used & new: US$63.00
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Asin: 0387944427
Average Customer Review: 5.0 out of 5 stars
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This is the first part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus.

The second part of this textbook has been published under the title, Applied Functional Analysis: Main Principles and Their Applications. ... Read more

Customer Reviews (3)

5-0 out of 5 stars motivated , well written, easy to read , nearly complete
This is a incredible book on applied functional analyses.Every topic is motivated with an applied problem.The definitions are motivated either by the aplication or by the subsequent use.There are remainders showing you the inteconections between the subjects and finally the index and the Symbols index are both complete and very usefull.The book is not complete. However he missing subjects usually are in the other colection by the same author.

5-0 out of 5 stars Excellent account on modern operator theory
This well-written text covers the fundamentals of modern linear operator theory and points out most of its connections to other branches of mathematics and physics ( differential equations, integral equations,finite elements, elasticity, quantum mechanics, and more). It includes allthe basic theory on Banach spaces, Hilbert spaces, orthogonality, Fourierseries, etc., and a chapter on the PDE's of mathematical physics. Theexcercises are both illustrating and challenging. I find it useful forundergrads, graduate students, and as a reference for workingmathematicians. Must read companion volume 109 also.

Please check myother reviews in my member page (just click on my name above).

5-0 out of 5 stars Indispensible to any serious student of Mathematics!
Prof. Zeidler has done the world of mathematicians an incredible serviceby writing this book. It is self-contained, very lucid, beautifullyorganised, and actually takes the trouble to relate various topics to eachother. It makes the field of Functional Analysis more accessible tostudents taking their first course in it. It also is a handy reference forpracticing mathematicians. I loved the little schematics in the book whichpoint out connections between seemingly disconnected ideas. All in all- agreat book. If you don't have it, and are interested enough in Math to bereading this review- go buy it!!!! ... Read more

24. Functional Analysis
by P.K. Jain, O.P. Ahuja
Hardcover: 382 Pages (2010-03-15)
list price: US$50.00 -- used & new: US$46.00
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Asin: 1906574677
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Functional Analysis is based on the lecture notes of distinguished authors and is designed to cater to the needs of students who are yet to be exposed to the subject, as well as senior undergraduate- and graduate-level students at universities the world over.

The text begins with a preliminary chapter that establishes uniform notations and covers background material in real analysis, linear algebra, and metric spaces. It is followed by chapters on Normed and Banach Spaces, Bounded Linear Operators and Bounded Linear Functionals. This text also deals with the concept and specific geometry of Hilbert Spaces, Functionals and Operators on Hilbert Spaces, and an Introduction to Spectral Theory. The appendix provides an introduction to Schauder Bases. ... Read more

25. Functional Analysis in Clinical Treatment (Practical Resources for the Mental Health Professional)
Hardcover: 512 Pages (2007-02-12)
list price: US$76.95 -- used & new: US$65.80
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Asin: 0123725445
Average Customer Review: 5.0 out of 5 stars
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WIth the ongoing pressures for psychologists to practice evidence-based care, and the requirement insurance carriers have both for treatment goals, measurement of outcomes, and a focus on brief therapy, functional analysis provides a framework for achieving all of the above. Having proven itself in treating behavioral problems in education, functional analysis is now being applied more broadly to behavioral and psychologial disorders.

In his 1996 book (Functional Analysis in Clinical Psychology, Wiley UK), Sturmey applied the functional behavioral approach to case formulation across a wide range of psychological disorders and behaviors. Since the publication of his book, no other volume has taken an explicit behavioral approach to case formulation. The changes that have occurred over the last 10 years in behavioral case formulation have been significant and substantial. They include (a) a large expansion of the range of problems addressed, such as ADHD, (b) a range of new verbal behavior therapies such as Acceptance and Commitment Therapies, (c) increased area of activity in the area of autism spectrum disorders; (d) many publications in how to train professionals, staff and parents in behavioral technology, and (e) new assessment instruments and procedures.

*Makes theories of functional analysis accessible to a wide range of mental health professionals
*Reviews behavioral assessment methods and strategies for case formulation
*Offers readers a practical, organized, data-based means of understanding psychiatric conditions for intervening effectively and measuring positive change ... Read more

Customer Reviews (1)

5-0 out of 5 stars An helpful tool to clinicians in behavior analysis
The book edited by Dr. Sturmey, at the same time provides us with an excellent explanation regarding struturalists and functionalists approaches, and talks about several types of behaviors classified as psychiatric. This text presents the analysis of the contingencies that can determine psychiatric problems as well as the radical behavioristic's interpretationof those behaviors and the treatment proposed due to that interpretation. It is an useful tool for clinicians and teachers that work with behavior therapy or even for applied behavior analysts. ... Read more

26. Functional Analysis (Springer Classics in Mathematics)
by Kosaku Yosida
Paperback: 501 Pages (1996-04-30)
list price: US$69.95 -- used & new: US$49.00
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Asin: 3540586547
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This volume, part of the Springer classics in mathematics series, looks at functional analysis. ... Read more

27. Functional Data Analysis (Springer Series in Statistics)
by Jim Ramsay, B. W. Silverman
Paperback: 430 Pages (2010-11-02)
list price: US$109.00 -- used & new: US$87.00
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Asin: 1441923004
Average Customer Review: 4.5 out of 5 stars
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This is the second edition of a highly succesful book which has sold nearly 3000 copies world wide since its publication in 1997.

Many chapters will be rewritten and expanded due to a lot of progress in these areas since the publication of the first edition.

Bernard Silverman is the author of two other books, each of which has lifetime sales of more than 4000 copies. He has a great reputation both as a researcher and an author.

This is likely to be the bestselling book in the Springer Series in Statistics for a couple of years.

... Read more

Customer Reviews (6)

5-0 out of 5 stars first good treatment of the topic and the theory behind the applications
Bernie Silverman is a great writer. Once again along with Ramsay he has written a very accessible book on an interesting but difficult topic. Functional data are series of curves. These kinds of data are often treated under the topic of longitundal data analysis and of course they can also be put under the general category of mutlivariate analysis. Because the x axis often represents time you may also view the analysis of these data as falling in the category of multivariate time series.
Jon Ramsay is a professor of psychology who has contributed to the research in multivariate analysis and has a lot of experience with important applications of functional data analysis. He has had many major publications on this topic in leading statistical journals and has made advances in curve registration and in the development of principal differential analysis.

What is exploited in the functional data analysis approach is the treatment of families of such functions through basis functions (wavelets, Fourier series, orthogonal polynomials etc.). The canonical example is a group of adult males whose growth curves are under study. Each curve has a similar shape but each individual has some differences in the asymptote and other parameters of the curve. Defining these parameters, chosing the approximating functions and assessing the fit to the data are all part of art of functional data analysis.

Silverman is an expert in smoothing and kernal density techniques and you will see his expertise and research contribution exhibited in this text. The roughness penalty approach is one method covered in this book and in more detail in a Chapman and Hall monograph with Green.

Registration of curves is a particular technique that is unique to functional data analysis. Other techniques discussed in the book are generalizations or extensions of existing multivariate techniques such as principal components and canonical correlations.

Shape and smoothness of a curve can be described through derivatives and so differential operators play an important role in functional data analysis. It has a chapter devoted to it and another chapter on a technique called principal differential analysis.

The book concludes with a forward looking chapter on the future of functional data analysis and the challenges that remain ahead.

Also look at the fine review on amazon by dataguru who emphasizes the exploratory aspects of the approach presented in this text and the need to have some knowledge of spline functions.

4-0 out of 5 stars great elementary reference
this is a great first book on introductory functional data analysis. the strength of the book lies in the fact that it introduces all concepts intuitively at first, without overwhelming the reader with any formalities. for the more mathematically minded reader, this a good introduction to the subject, which can be later complemented with more formal textbooks on functional analysis.

5-0 out of 5 stars Very clear introduction to functional data analysis
Functional data analysis is a topic of increasing interest in the statistics community, and is most commonly applied to time-series and/or spatial-series data. The main idea is to begin one's analysis of the data by constructing a smoothed or interpolated version, and then do many of the standard statistical things (such as finding principle components or doing regressions) in that smoothed function space.

The book explains the ideas and methods behind functional data analysis very clearly, with a minimum of math and notation and with a number of recurring, illustrative examples. For those interested in quickly getting oriented to the basic concepts and perhaps trying them out, I found that a few days with this book is a good place to start. The authors have also published a book with more detailed applications worked out called "Applied Functional Data Analysis".

4-0 out of 5 stars fine introduction to the topic
FDA is a very important new topic in statistics and Ramsay and Silverman provide an accessible introduction to the topic.

Functional data occur when the data are curves.For instance, we might monitor growth of children sampled at a fairly fine grid over several years.Or we might consider reports of experienced pain in many patients over a fairly long period of time.Even when the data *seem* discrete (and given measurement error and a finite sampling rate all data really *are* discrete) there may be substantial advantages to treat them as continuous.

Functional analysis extends the notion of linear space that is the foundation of statistics to the infinite dimensional case.In a infinite dimensional space, a matrix equation becomes an integral equation, and so on.They provide a useful introduction to the topic, enough that a non-specialist can get into it.The big difference between this treatment and older ones is that Ramsay and Silverman emphasize that the data generating process is assumed to be continuous.Many older treatments of similar data involve no curve regularization or smoothing.Basically they ignore the underlying continuity.Ramsay and Silverman show there are substantial benefits to paying attention to the continuity.For instance, if we want to estimate the derivative of a sampled curve it's logical to use first differences.They demonstrate, however, that fitting a smooth to the curve, e.g., a spline, and then finding the derivative of the smooth curve often does a much better job.(Why?Differencing amplifies noise.)

Anyway, they cover topics of linear models, principal components, canonical correlation, and principal differential analysis in function spaces.Their general feel is fairly exploratory.The one thing this book is short of is long examples, which can be found in their companion volume Applied Functional Data Analysis.

5-0 out of 5 stars First book on an important subject
This book deals with statistical analyis of multivariate data which may betreated preferably as curves. Examples of such situations includemultivariate time series data which are observed at unequally spacedintervals, andtwo-way data in social sciences, and many high-dimensionaldata.Since this is the first attempt at a systematic account of thisrapidly growing area, it wisely chooses to focus on descriptiveandexploratory techniques developed by the authors and others.The readersare well-advised to have some background on smoothing spline which isemployed as the key modeling framework.

For curious readers like me, itstill leaves more to be desired. For example, the theory is better preparedby Grenander (1981)'s Abstract Inference, while the practice is preceded bythe vast work on analysis of space-time field (4-D var) in climate researchusing EOF, similar to the principal components, but applied to the 2-dfield data. I would also like to see more discussion of alternativemodeling techniques such as wavelets and kernel smoothing methods.

Ifind this book a handy reference, so would recommend to others for the samepurpose. ... Read more

28. Nonlinear Functional Analysis and Its Applications: Part 2 A: Linear Monotone Operators (Zeidler, Eberhard//Nonlinear Functional Analysis and Its Applications)
by E. Zeidler
Hardcover: 467 Pages (1989-12-11)
list price: US$179.00 -- used & new: US$116.10
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Asin: 0387968024
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This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text.

The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century. ... Read more

29. Applied Functional Data Analysis
by J.O. Ramsay, B.W. Silverman
Paperback: 200 Pages (2002-06-13)
list price: US$89.95 -- used & new: US$55.99
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Asin: 0387954147
Average Customer Review: 5.0 out of 5 stars
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What do juggling, old bones, criminal careers and human growth patterns have in common? They all give rise to functional data, that come in the form of curves or functions rather than the numbers, or vectors of numbers, that are considered in conventional statistics. The authors' highly acclaimed book Functional Data Analysis (1997) presented a thematic approach to the statistical analysis of such data. By contrast, the present book introduces and explores the ideas of functional data analysis by the consideration of a number of case studies, many of them presented for the first time. The two books are complementary but neither is a prerequisite for the other. The case studies are accessible to research workers in a wide range of disciplines. Every reader, whether experienced researcher or graduate student, should gain not only a specific understanding of the methods of functional data analysis, but more importantly a general insight into the underlying patterns of thought. Some of the studies demand the development of novel aspects of the methodology of functional data analysis, but technical details aimed at the specialist statistician are confined to sections which the more general reader can safely omit. There is an associated web site with MATLAB and S-PLUS implementations of the methods discussed, together with all the data sets that are not proprietary. Jim Ramsay is Professor of Psychology at McGill University, and is an international authority on many aspects of multivariate analysis. He was elected President of the Statistical Society of Canada for the term 2002-3 and is a holder of the Society's Gold Medal for his work in functional data analysis. His statistical work draws on his collaborations with researchers in speech articulation, biomechanics, economics, human biology, meteorology and psychology. Bernard Silverman is Professor of Statistics at Bristol University. He was President of the Institute of Mathematical Statistics in 2000-1 and has held various offices in the Royal Statistical Society. He is a Fellow of the Royal Society and a member of Academia Europaea. His main specialty is computational statistics, and he is the author or editor of several highly regarded books in this area. He has also published widely in theoretical and applied statistics, and in many other fields, including law, human and veterinary medicine, earth sciences and engineering. ... Read more

Customer Reviews (2)

5-0 out of 5 stars Optional complement for 'FunctionalData Analysis'
A nice, if overpriced, book, but not one that you need to keep, unlike Ramsay and Silverman's "FunctionalData Analysis" (FDA). AFDA elaborates several examples introduced in FDA. The examples cover about 60% of FDA's material: smoothing is given much less space than in FDA, and regression (cf. FDA's Chapters 12-15) is left out. If you are choosing between the two books, go for FDA.

5-0 out of 5 stars teaching functional data analysis through examples
In 1997 Ramsay and Silverman wrote a standard text that stands out as a classic book teaching the functional approach. With this new book they take the approach of teaching by example.

Each of chapters 2-12 present a case study first. The one on childhood growth is standard fair but they also present unusual cases such as modeling a juggler and analyzing handwriting. In eachcase they show how special characteristics of the data are best portrayed by treating curves or functions as individual data points. The application is presented first. Then the authors show how as consultants they formuated a functional data approach to the problem. Sometimes transformations are applied first. In another case principal component curves are constructed. After each problem is presented with the approach taken, the authors go back and present a "what we have seen" section that reviews the key points and lessons learned from the examples.

This is a wonderful way to make the material very accessible to practitioners as well as statisticians and it illustrates the variety of problems and that can be handle by this approach to data analysis.

... Read more

30. Introductory Real Analysis
by A. N. Kolmogorov, S. V. Fomin
 Paperback: 416 Pages (1975-06-01)
list price: US$15.95 -- used & new: US$8.00
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Asin: 0486612260
Average Customer Review: 4.0 out of 5 stars
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Comprehensive, elementary introduction to real and functional analysis. Self-contained, readily accessible to those with background in advanced calculus. Cover basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, much more. 350 problems.
... Read more

Customer Reviews (32)

4-0 out of 5 stars Clarity and examples
This is a clearly written book with lots of examples at an amazingly low price. I once asked a professional economist what books would cover the math used in his work and he pulled two books off his shelf, Kolmogorov/Fomin's Analysis and Luenberger's Optimization. So I tend to think pretty highly of this book in terms of usefulness. That said it's tough to go through as the authors don't spend much time on motivation and seem to jump from topic to topic. I found it easier to understand on a second perusal after I had taken an analysis course.

4-0 out of 5 stars Good intermediate math book
This is a very good intermediate math book. I used it to write my undergraduate monograph and it actually helped a lot (I'm an economics student). However, it is difficult to understand without the help of other books. In fact, if you want to use this book I recommend to get also: "Topology" by Munkres and "The Way of Analysis" by Robert Strichatz. They all make a very useful math kit and if you are thinking in a Ph.D. in economics they can help you a lot if you read them (not all, buy selected chapters) before you start the math review at the begining of the Ph.D. program.

1-0 out of 5 stars DON'T buy this book!
This is not the original work. Just like Emily Dickinson's poems, sometimes you get an "edited" version of a beautiful mathematical work. I am SO sorry that I bought this book. Besides the problem with messing with a finished work, there are serious errors in proofs all over the book.

Get Elements of the Theory of Functions and Functional Analysis instead (also by Dover).

4-0 out of 5 stars Not A Bad Book
I didn't like this book at first because it wasn't what I expected. I think the word "introductory" should be removed from the title. It's actually not an introductory book. I would recommend this book for graduate studies. Most real analysis courses at the graduate level focus on the measure theory and integration. However, I appreciate this book more now.

3-0 out of 5 stars A good read with too many mistakes
The advantages of this text have been pointed out by other readers, so I will attempt to exhibit the problems of this book.

There are a lot of mistakes. And by 'a lot', I mean that the careful reader should be able to find at least 5 mathematical mistakes in each chapter. I used this text mainly as a supplement to a fairly advanced analysis course, and we'd often have problems from it used in our problem sets. At first, it appeared as if this were a very well-written text, but once we started with our problem sets, there were at least 2 e-mails sent out per week addressing a concern a student had pointed out. After a while, students stopped e-mailing the professor with their concerns, instead just assuming that they were correct whenever they spotted something weird.

Let's take an example:

Problem 1, pg. 137: Let M be the set of all points x = (x1, x2, ..., xn, ...) in l2 satisfying the condition \sum^{\infty}_{n=1} (n^2) (x_n)^2 \le 1. Prove that M is a convex set, but not a convex body.

The problem with this is that M IS easily a convex body, precisely because x = (0,0,...) is in M.

There are many more big mistakes and little mistakes throughout the exercises, oftentimes destroying the entire POINT of the problem. Take, for example, Problem 1 of pg. 76: Let A be a mapping of a metric space R into itself. Prove that the condition p(Ax,Ay) < p(x,y) (x\ne y) is insufficient for the existence of a fixed point of A.

Now, a counterexample here can be easily produced, even by the most elementary reader. But the exercise quickly becomes worthwhile if we make R complete. It's the little things that count in mathematics, and the small errors like these are clearly detrimental to the student.

But the errors in the text aren't limited to exercises. I was reading independently at the front of the book to get some info on Zorn's Lemma and ordinal numbers, and as I read, I found the following definition:

Let M1 and M2 be two ordered sets of type 01 and 02, respectively. Then we can introduce an ordering in the union M1 U M2 of the two sets by assuming that

1) a and b have the same ordering as in M1 if a,b are in M1
2) a and b have the same ordering as in M2 if a,b are in M2
3) a < b if a in M1, b in M2

The set M1 U M2 ordered in this way is called the ordered sum of M1 and M2, denoted by M1 + M2.

There is a clear problem with this definition pointed out here: http://www.physicsforums.com/showthread.php?t=200985. How is the student expected to learn such important material when even the definitions have loopholes?By the end of our experience with this book, our professor was giving out exercises to correct Kolmogorov/Fomin's incorrect definitions.

Note also that Silverman uses very weird words. For example, 'countably compact' is used instead of 'sequentially compact'. ... Read more

31. S+Functional Data Analysis: User's Manual for Windows ®
by Douglas B. Clarkson, Chris Fraley, Charles Gu, Jim Ramsay
Paperback: 194 Pages (2005-07-01)
list price: US$69.95 -- used & new: US$35.88
(price subject to change: see help)
Asin: 0387249699
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S+Functional Data Analysis is the first commercial object oriented package for exploring, modeling, and analyzing functional data. Functional data analysis (FDA) handles longitudinal data and treats each observation as a function of time (or other variable). The functions are related. The goal is to analyze a sample of functions instead of a sample of related points.

FDA differs from traditional data analytic techniques in a number of ways. Functions can be evaluated at any point in their domain. Derivatives and integrals, which may provide better information (e.g. graphical) than the original data, are easily computed and used in multivariate and other functional analytic methods.

The analyst using S+FDA can handle irregularly spaced data or data with missing values. For large amounts of data, working with a functional representation can save storage. Moreover, S+FDA provides a variety of analytic techniques for functional data including linear models, generalized linear models, principal components, canonical correlation, principal differential analysis, and clustering.

This book can be considered a companion to two other highly acclaimed books involving James Ramsay and Bernard Silverman: Functional Data Analysis, Second Edition (2005) and Applied Functional Data Analysis (2002). This user's manual also provides the documentation for the S+FDA library for S­Plus.

From the reviews:

"The book offers an overview of the basics of functional data approaches as well as a weath of information, sample code, and examples about each of these methods in a clear well-presented manner. The book provides a well-written discussion of how and when to use the functions, and it will be a useful and convenient reference for those getting started with functional analyses." The American Statistician, May 2006, Vol. 60, No. 2

... Read more

32. Beginning Functional Analysis (Undergraduate Texts in Mathematics)
by Karen Saxe
Paperback: 197 Pages (2010-11-02)
list price: US$59.95 -- used & new: US$44.56
(price subject to change: see help)
Asin: 1441929142
Average Customer Review: 3.5 out of 5 stars
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The unifying approach of functional analysis is to view functions as points in abstract vector space and the differential and integral operators as linear transformations on these spaces. The author's goal is to present the basics of functional analysis in a way that makes them comprehensible to a student who has completed courses in linear algebra and real analysis, and to develop the topics in their historical contexts. ... Read more

Customer Reviews (7)

5-0 out of 5 stars Whirlwind tour of functional analysis
This is a concise and well-written introduction to functional analysis. It manages to cover all the major results, as well as developing the theory of Lebesgue integration, in a mere 180 pages. It accomplishes this concision primarily by being very selective: it covers only the most important and most interesting results. It is aimed at upper-level undergraduates, but will be useful to anyone who always wanted to learn functional analysis but did not have the patience to plow through one of the popular multi-hundred-page tomes.

This is not an easy book, and many of the proofs are very brief. The whole theory of Lebesgue integration, including measure theory and the convergence theorems, is developed in 25 pages. There are so many different topics that it sometimes seems fragmented.

Like many functional analysis books, this one does not say much about the applications, and much of the narrative seems unmotivated. The applications are alluded to from time to time, and the book does gives references where more information on applications can be found. Except for the weak coverage of applications, the book does a very good job of placing functional analysis in historical and mathematical context, with biographical profiles of the main researchers in the field and discussions of the historical order in which things were discovered (and rediscovered). The book has about 130 references spread throughout the text where more details can be found; many of these references are to expository, survey, and historical works rather than to research papers.

3-0 out of 5 stars Makes the material unnecessarily dry and boring
I do not agree with the other readers that say this book moves too quickly or is too difficult--your first couple encounters with the UTM series often always seem this way.However, I don't think this is the best introductory book on the subject material for a number of reasons.The other reviewers make clear that less experienced students do not find this book easy--I am pointing out that a more experienced student finds this book boring.

I feel that functional analysis, like linear alegbra, is one subject in mathematics that is often not sufficiently motivated, and as a result comes across as both difficult and boring.While I think this book takes some of the difficulty out of things through its straightforward and clear explanations of various concepts, and through its relatively easy exercises which reinforce the material, I find this book to be exceptionally boring, especially in the initial few chapters.The book is too concise for a UTM text; it's hard for students to understand why to get through the earlier material unless you give more interesting examples and talk a little bit more about where you're going and why anyone would want to learn this stuff.

I would recommend the book by Kreyszig as a supplement to anyone stuck reading this one; it doesn't cover the same material (it tends to be a little less advanced, omitting discussion of measures), and it's a very different sort of book, but especially in the earlier few chapters it will provide a much needed energy, more interesting examples.

2-0 out of 5 stars Not helpful
I wouldn't call this an undergrad text. It's more advanced and moves faster than Rynne & Youngson. In an effort to cover a lot without much prerequisites, it moves too fast, introducing a lot of basic ideas in an offhand way. I found the explanations generally not as clear as in related books. No examples, few hints, no answers.

2-0 out of 5 stars I'm Sorry
I'm sorry I had to read this book, I'm sorry anyone else had to read this book, and I hope that no one else has to suffer through this book.Pedagogically speaking, it is un-sound to state, in the first chapter and in the first several pages, a theorem and, rather than set a tone and rhytmn for the book, good 'ole Saxes leaves these theorems to the reader as exercises.Now, Saxe is not Lang and the Springer book series, namely, undergraduate texts, is just that, for undergraduates, for young students, mathematically speaking, and hence such an adverse and lazy tone should not be set in such a book.Furthermore, her direction, her flow, her in-ability to illuminate and bring forth the beauty of Functional Analysis is depressing (see Ascoli's Theorem and, while your seeing things, maybe Saxes should have seen an editor).For those of you who have had some Analysis, are familiar with basic point-set topology, and have a general idea of what it means for a mapping between to spaces to be linear, then the book you should read is that of Erwin Kreyszig.This book provides you with all the necessary tools as well as motivated and complementary exercises (some solutions are provided).Steer far away from Saxe's book.As an aside, it is obvious that no book, and hence no author, is perfect or capable of producing a 'perfect' book.The problem that arises in the case of the current book being reviewed is that considerable knowledge and or passion for a given subject does not necessarily imply that you are capable of re-casting this knowledge in the form of a book.Maybe, just maybe, if there is a future reprint, hopefully, Saxe will be able to re-work the book and create something hjigher in quality.Until that time, go else-where if you are interested inl earning Functional Analyiss.

1-0 out of 5 stars Quite a bad book.
A lot of bla bla in this book. This book is a collection of noteswithout a guideline in mind. The more interesting subjects of functional analysis are only superficially treated. Proofs are often quite shortly illustrated and in a proof I found a gigantic error. Not worth to buy this book. ... Read more

33. Linear Functional Analysis (Springer Undergraduate Mathematics Series)
by Bryan Rynne, M.A. Youngson
Paperback: 324 Pages (2007-12-11)
list price: US$49.95 -- used & new: US$31.95
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Asin: 1848000049
Average Customer Review: 4.0 out of 5 stars
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This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material.

The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.

Further highlights of the second edition include:

a new chapter on the Hahn–Banach theorem and its applications to the theory of duality. This chapter also introduces the basic properties of projection operators on Banach spaces, and weak convergence of sequences in Banach spaces - topics that have applications to both linear and nonlinear functional analysis;

extended coverage of the uniform boundedness theorem;

plenty of exercises, with solutions provided at the back of the book.

... Read more

Customer Reviews (2)

5-0 out of 5 stars Great Introductory Supplement
I highly recommend this book for independent study or as a supplement to a text. You can see if you're on the right track with exercises because the text has solutions and hints in the back. People must keep in mind that this book focuses on linear functional analysis and not functional analysis in general.

3-0 out of 5 stars Clear, basic introduction
This undergrad text is extremely clear, with lots of examples and exercises. I thought the coverage was a bit limited, even for an undergrad text and the writing style is kind of dry. Still, it's perhaps even easier than Kreyszig. ... Read more

34. Functional Analysis - Applications in Mechanics and Inverse Problems (Solid Mechanics and Its Applications)
by L. P. Lebedev, I.I. Vorovich, G. M. L. Gladwell
Paperback: 260 Pages (2002-06-01)
list price: US$69.95 -- used & new: US$48.99
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Asin: 1402007566
Average Customer Review: 5.0 out of 5 stars
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This is a book for people who want to use functional analysisto justify approximate methods in Mechanics and Inverse Problems. Itprovides such researchers with the tools they need without having toassimilate or skip through concepts they do not need.For the applied mathematician, the essential difficulty attending thestudy of functional analysis is that the pure mathematicians who havedeveloped the field have carried the process of abstraction, which isthe essence of functional analysis, to increasingly higher levels. Inthis book, the authors have kept the level of abstraction high enoughfor the majority of applications, and have resisted the temptation toabstract to the limit.The book can be used for a lecture course or for self study; there areexercises throughout, and references for further study.This new edition corrects a number of typographical and logical errorsin the first edition. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Exceptional book -- strongly recommended
Aimed at students in applied mathematics, physics, and engineering, this book is of exceptional quality: lucid, self-contained, friendly in style. I believe it represents an unmatched opportunity for modern engineers to learn applied functional analysis. Known for his pioneering work in shell theory, Prof Vorovich was a national prize winner and member of the Russian Academy of Sciences. Highly recommended! ... Read more

35. Real Analysis (4th Edition)
by Halsey Royden, Patrick Fitzpatrick
Hardcover: 544 Pages (2010-01-15)
list price: US$132.00 -- used & new: US$95.00
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Asin: 013143747X
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Real Analysis, Fourth Edition, covers the basic material that every reader should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in mathematics and familiarity with the fundamental concepts of analysis.


Classical theory of functions, including the classical Banach spaces; General topology and the theory of general Banach spaces; Abstract treatment of measure and integration.


For all readers interested in real analysis. ... Read more

36. Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
by Frédéric Ferraty, Philippe Vieu
Paperback: 268 Pages (2010-11-02)
list price: US$109.00 -- used & new: US$87.00
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Asin: 1441921419
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Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. At the same time it shows how functional data can be studied through parameter-free statistical ideas, and offers an original presentation of new nonparametric statistical methods for functional data analysis.

... Read more

37. Functional Analysis And Semi-Groups
by Einar Hille
Hardcover: 268 Pages (2008-11-04)
list price: US$40.95 -- used & new: US$40.95
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Asin: 1443721670
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Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork. ... Read more

38. Signs and Symptoms Analysis from a Functional Perspective
by Dicken Weatherby
Paperback: 506 Pages (2004-10-24)
list price: US$65.00 -- used & new: US$40.95
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Asin: 0976136724
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This book presents a diagnostic system of signs and symptoms analysis that focuses on the most important questions you should be asking your patients. The questions are organized by body systems and will help you gather more information on the functional state of your patients. Whether you are well-seasoned doctor, fresh from medical school, or a patient looking for answers to your questions you will refer to this book again and again.

You will discover how easy it is to identify where the symptom burden is located in the body, increase your efficiency of history taking in the office, implement new tools and techniques to dramatically improve your clinical outcomes, cut the amount of time you spend taking a patient history, and make your initial history an indispensable screening tool. Your signs and symptoms analysis will finally mean something to you and your patients.

This book includes:
In depth information on each of the questions on the questionnaire.
Complete instructions for doing a manual assessment.
A full section on diet, lifestyle and medications explaining their effects on your patients’ health.
Full details on functional tests to gather even more information from your patients.
24 handouts for your patients, including food sources of nutrients, alternatives to common food allergens and diets for many functional disorders.
Improve your clinical efficiency by identifying how your treatment is progressing over time.

Master forms of 322 question questionnaire and manual symptom burden analysis form available as a download.

This best selling manual on Signs and Symptoms Analysis has shown hundreds of doctors how to do a functionally oriented history. What are you waiting for? ... Read more

39. Elementary Functional Analysis
by Charles Swartz
Hardcover: 192 Pages (2009-07-13)
list price: US$45.00 -- used & new: US$41.00
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Asin: 9814273341
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This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

  • Normed Linear and Banach Spaces
  • Linear Operators
  • Quotient Spaces
  • Finite Dimensional Normed Spaces
  • Inner Product and Hilbert Spaces
  • The Hahn Banach Theorem
  • Applications of the Hahn Banach Theorem to Normed Spaces
  • The Uniform Boundedness Principle
  • Weak Convergence
  • The Open Mapping and Closed Graph Theorems
  • Projections
  • Schauder Basis
  • Transpose and Adjoints of Continuous Linear Operators
  • Compact Operators
  • The Fredholm Alternative
  • The Spectrum of an Operator
  • Subdivisions of the Spectrum
  • The Spectrum of a Compact Operator
  • Symmetric Linear Operators
  • The Spectral Theorem for Compact Symmetric Operators
  • Symmetric Operators with Compact Inverse
  • Bounded Self Adjoint Operators
  • Orthogonal Projections
  • Sesquilinear Functionals
  • The Spectral Theorem for Bounded Self Adjoint Operators
  • An Operational Calculus
  • The Spectral Theorem for Normal Operators
... Read more

40. Applied Functional Analysis (Applications of Mathematics)
by Alampallam V. Balakrishnan
 Hardcover: 373 Pages (1981-05-04)
list price: US$69.80 -- used & new: US$69.80
(price subject to change: see help)
Asin: 0387905278
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