Product Description
This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be suitable for a course in functional analysis. The book also includes applications to partial differential equations, the stability and stabilization of linear systems, power signal spaces, and delay systems, treated from an input/output point of view. ... Read more

Product Description
This is one of the few books available in the literature that contains problems devoted entirely to the theory of operators on Banach spaces and Banach lattices. The book contains complete solutions to the more than 600 exercises in the companion volume, An Invitation to Operator Theory, Volume 50 in the AMS series Graduate Studies in Mathematics, also by Abramovich and Aliprantis.

The exercises and solutions contained in this volume serve many purposes. First, they provide an opportunity to the readers to test their understanding of the theory. Second, they are used to demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Third, the exercises include many well-known results whose proofs are not readily available elsewhere. Finally, the book contains a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible.

The book can be very useful as a supplementary text to graduate courses in operator theory, real analysis, function theory, integration theory, measure theory, and functional analysis. It will also make a nice reference tool for researchers in physics, engineering, economics, and finance. ... Read more

Product Description
A new, updated and enhanced edition of the classic work, which was welcomed for its general approach and self-sustaining organization of the chapters.

Written by a highly respected textbook writer and researcher, this book has a more general scope and adopts a more practical approach than other books. It includes applications of condensed matter physics, first developing traditional concepts, including Feynman graphs, before moving on to such key topics as functional integrals, statistical mechanics and Wilson's renormalization group. The author takes care to explain the connection between the latter and conventional perturbative renormalization. Due to the rapid advance and increase in importance of low dimensional systems, this second edition fills a gap in the market with its added discussions of low dimensional systems, including one-dimensional conductors.

All the chapters have been revised, while more clarifying explanations and problems have been added. A free solutions manual is available for lecturers from www.wiley-vch.de/textbooks. ... Read more

Customer Reviews (2)

Extremely solid for self-teaching
This book is an ideal introduction to quantum field theory for a graduate student. Assuming a strong background in basic quantum mechanics and classical mechanics, Huang develops quantum field in a methodical fashion. In contrast to other popular quantum field theory books (such as Peskin) Huang doesn't leave out important details, especially with regard to the mathematics behind spinor fields. Plus the book is very readable.

A good introduction to the physics behind renormalization
A very good introduction to QFT. It starts with a rather classical account of QED, then develops renormalization and applies it mainly to statistical physics. So the text does not cover non-abelian gauge theories, and is notsufficient for readers who learn QFT for particle physics applications. Butthe exposition of renormalization is really excellent and complete. I likedthe exceptional clarity and lucidity of most calculations, and theexcellent set of problems. Solving them all extends the book's scope farbeyond the table of contents. ... Read more

Product Description
This classic textbook by two mathematicians from the U.S.S.R.’s prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
... Read more

Customer Reviews (2)

A Dover classic.
The spectral theorem of David Hilbert, John von Neumann, and Marshall Stone gives a complete answer to the question of which operators admit a diogonal representation, up to unitary equivalence, and makes the question precise as well. The theorem states that these are the normal operators in Hilbert space. This includes the selfadjoint operators which represent observables in quantum physics, and the more interesting ones are unbounded. Remember the Heisenberg commutation relations do not admit bounded solutions. But there is a mathematical distinction between formally selfadjoint operators (also called symmetric operators) and the selfadjoint ones. It is only the latter to which the spectral theorem applies. The distinction between the two is understood from a pair of indicies (n,m), now called deficiency indices. In some applications they represent
boundary conditions, and when n = m, and the boundary conditions are assigned, the symmetric operator in question has selfadjoint extensions. And we know from von Neumann what they are. A central question in the book concerns the issue of unequal indices. Then selfadjoint extensions do not exist, at least not unless the Hilbert space is enlarged. A central theme in the book is that in case of unequal indices, there is a larger Hilbert space which does in fact admit selfadjoint extensions. The co-authors, along with Naimark, are the authorities on this. Because of applications to PDE theory and to physics, there has been constant interest in the theme right up to the present. Even the current interest, and lively activity, in quantum measurement theory (in connection with quantum information theory) and entanglement brings back to to the fore this old issue around diagonalizing operators by passing to an "enlarged" (or dilated)Hilbert space, or looking for an orthonormal basis in the extended Hilbert space. So the theme of the book is still current.

Such an easy book to read!
This is a great intro to functional analysis. Having taken a graduate course on the subject, I used this as my text. The proofs are very readable and kept clear and simple. You'll see the subject develop before your eyes.One thing: when reading this book on infinite dimensional vector spaces,always try to draw a parallel with the finite dimensional version of thesubject, linear algebra. You'll appreciate the book all the more. For everytheorem relating to a bounded linear operator on Hilbert space, replace theoperator by a matrix on Euclidean n-space.. you'll say "oh yeah! Iremember that from linear algebra!" ... Read more

Product Description
This work and Fundamentals of the Theory of Operator Algebras. Volume I, Elementary Theory present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences. ... Read more

Customer Reviews (1)

A top book in operator algebra
This book contain 14 Chapter in 2 volume. In v.1 the authours detailed the elementary property of operators and operator algebra in Hilbert spaces. In volume 2 the authours investigate more advance results and detail on some concepts such as cross product and direct integral of Hilbert spaces. ... Read more

Product Description

The book is a commemorative volume honoring the mathematician Paul R. Halmos (1916-2006), who contributed passionately to mathematics in manifold ways, among them by basic research, by unparalleled mathematical exposition, by unselfish service to the mathematical community, and, not least, by the inspiration others found in his dedication to that community.Halmos made fundamental contributions in several areas of mathematics.

This volume emphasises Halmos's contributions to operator theory, his venue for most of his mathematical life. The core of the volume is a series of expository articles by prominent operator theorists providing an overview of how operator theory prospered during the Halmos era, in no small measure thanks to Halmos's leadership and penetrating insights.

Product Description

This EMS volume contains a survey of the principles and advanced techniques of the spectral theory of linear differential and pseudodifferential operators in finite-dimensional spaces. Also including a special section of Sunada's recent solution of Kac's celebrated problem of whether or not "one can hear the shape of a drum".

Product Description
Vol. 1 of Lars Hörmander's influential 4-volume treatise is a detailed exposition of the theory of distributions. From the reviews: 'In order to illustrate the richness of the book: in my review of the 1983 edition [...] I gave a list of 20 subjects which were new compared to Hörmander's book of 1963. Most of these subjects concern important, basic and highly nontrivial theorems in analysis. Hörmander's treatment of these is extremely clear and efficient and often highly original. [...] Most of the exercises are witty, with an interesting point. The phrasing of both the exercises and the answers and hints is very careful [...] In all, the book can be highly recommended, both as a textbook for advanced students, and as background and reference for introductory courses on distributions and Fourier analysis. J.J. Duistermaat in Mededelingen van het Wiskundig Genootschap. ... Read more

Customer Reviews (1)

the definitive guide to micro-local analysis
Hormander's four volume guide to linear partial differential operators is the definitive guide to smooth micro-local analysis from the man who invented a large fraction of it.

Micro-local analysis is an approach tothe analysis of singularities of variable coefficient linear partialdifferential equations based on the use of the Fourier transform and ofsymplectic geometry. Ideas from Hamiltonian physics and quantum theory alsofeature heavily. The fact that the subject is a mixture of analysis andgeometry makes it beautiful and powerful.

The four volume set is hardwork and in some ways is more useful as a reference work than as a learningbook but on the other hand, all the material is there and the books doreward the reader who is willing to spend the time to study themcarefully.

The first volume is the most accessible and the secondpaperback edition carries the added benefit of included exercises withpartial answers which are often highly informative. ... Read more

Product Description

The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications.

From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS

Customer Reviews (1)

A definitive work marred by cheap production techniques
I've been examining this book carefully for the last several weeks for possible use in a nonlinear analysis course I am constructing at Brigham Young University.All the positive things that the professional reviews say are true:this is really a remarkable work!

But here's the problem:If you order this book now, you will probably receive a low-grade digital reprint, as I did when my copy arrived from Amazon this afternoon.Gone is the sturdy sewn binding of the original printing, the graphics now look like they were produced on a 1980s vintage dot matrix printer, and the digital reprinting process makes it even difficult to tell bold from regular type.Advanced mathematics uses symbols with fine detail; the more difficult that detail is to discern, the more difficult the content is to absorb.To present the fine work of Dugundji and Granas in this inferior format is a travesty.

Publishers freely acknowledge the difference between hardcover and softcover books in their advertising and pricing; why won't they do the same when it comes to the difference between an original printing and a digital reprint?

I sent my copy back for a refund, and I'll refrain from purchasing any more math texts that have been given this "digital printing" treatment in the future.To the extent that I am aware of their status, I will also henceforth refrain from adopting such texts for courses I teach.I'm probably tilting at windmills, but these cheap knockoffs are apparently becoming more and more common, and if there's even a slight chance of getting publishers to think twice about cutting corners like this, it will be worth it.

[December 2009 Update:The author has contacted me about my previous 2-star rating hurting his sales, so I have changed the rating to 5-stars, even though "I don't like it" still captures my feelings about this book as Springer is currently producing it.I will not buy it in its current state.]
... Read more

Product Description

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Product Description
This timely volume examines current developments in nonlinear analysis emphasizing accretive and monotone operator theory -- including, for the first time in book form, a major survey/research article on partial differential equations with delay and an important survey/research article on approximation solvability. ... Read more

Product Description
K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory.This book is the only comprehensive treatment of K-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the theory of extensions, and Kasparov's bivariant KK-theory for C*-algebras. Special topics covered include the theory of AF algebras, axiomatic K-theory, the Universal Coefficient Theorem, and E-theory. Although the book is technically complete, motivation and intuition are emphasized. Many examples and applications are discussed. ... Read more

Customer Reviews (2)

A well-written book on a difficult subject
K-theory is a challenging subject; Kasparov's KK-theory even more so. But Bruce Blackadar's textbook manages to present both of these in a clear and coherent fashion, readable both by mathematicians and physicists. The ideal reader of this book will already be familiar with the basics of operator algebras and will have had some exposure to K-theory (perhaps through Wegge-Olsen's remarkable book) and noncommutative geometry; but an extensive background is not needed.

One especially good feature of this book is the wealth of examples it contains, especially those examples of most relevance to string theory. (Where K-theory is finding some of its most interesting applications today) A wide range of subjects such as "topological" K-theory (the K-theory of gauge fields) and supersymmetry (referred to as "grading," following mathematicians' notation) round out this presentation of one of the most exciting subjects on the border of mathematics and physics.

A difficult book on a difficult subject
The books covers not only K-theory but also KK-theory that was introduced by G. G. Kasparov. The original article by Kasparov are very hard to read because of the generality of his approach. Furthermore the theory was muchsimplified by Skandalis et al. The second part of the book offers a veryreadable introduction to KK-theory. Now the new edition even contains ashort exposition of E-theory.

"Elements of KK-theory" by K. K.Jensen and K. Thomsen is good introduction too. ... Read more

Product Description
In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work. ... Read more

Product Description
Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

Key Features

- Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
- Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
- Introduces each new topic with a clear, concise explanation.
- Includes numerous examples linking fundamental principles with applications.
- Solidifies the reader's understanding with numerous end-of-chapter problems.

· Provides an ideal transition between introductory math courses and advanced graduate study in applied mathematics, the physical sciences, or engineering.
· Gives the reader a keen understanding of applied functional analysis, building progressively from simple background material to the deepest and most significant results.
· Introduces each new topic with a clear, concise explanation.
· Includes numerous examples linking fundamental principles with applications.
· Solidifies the reader's understanding with numerous end-of-chapter problems. ... Read more

Product Description

The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized during the conference: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Product Description
The primary purpose of this book is to teach, and to enable readers to study the recent literature on this subject and its many applications. It is suitable for graduate-level courses in functional analysis and operator algebras, and as a reference for self-study by graduates. ... Read more