Book Description
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.
Customer Reviews:
typical expensive and unenlightening math text.......2006-11-08
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
definitions.
Functional analysis.......2006-02-23
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.
Excellent.......2004-02-20
Peter D Lax is one of the great mathematicians of the 2nd half of the 20th century. Buy this book if only to have it on your bookshelf. After a long day of suffering fools and putting up with the latest insanities of your university administrators, leaf through Lax's book to recover. This is mathematics at its best. What better use can we put mathematics to, than to help us regain our sanity in a world that's gone mad.
Brings the subject to life!.......2002-08-02
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. It 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. 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. Peter Lax has himself,-- alone and with others, shaped some of greatest successes of the period, right up to the present. That is in the book!! And it offers an upbeat outlook for the future. It has been tested in the class room,-it is really user-friendly. At the end of each chapter P Lax ofers personal recollections;-- little known stories of how several of the pioneers in the subject have been victims,- in the 30ties and the 40ties, of Nazi atrocities. The writing is crisp and engaged,- the exercises are great;- just
right for students to learn from. This is the book to teach from.
Average customer rating:
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Measure Theory and Integration (Pure and Applied Mathematics)
M.M. Rao
Manufacturer: Marcel Dekker
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A Modern Theory of Integration (Graduate Studies in Mathematics)
ASIN: 0824754018 |
Book Description
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition · provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals · contains extended discussions on the four basic results of Banach spaces · presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties · details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions · covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
Customer Reviews:
Jon's Review.......2002-04-18
Simply put, M.M. Rao's "Measure Theory and Integration" is an awesome book. It is truly the "Encyclopedia Britannica" of Real Analysis textbooks. This math textbook/reference book contains the most general, yet practical, theorems on the subject known to mankind. I cannot recommend it highly enough.
Book Description
This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
Customer Reviews:
Inspiring and Useful.......2000-06-13
I was turned on to this book by a friend of mine who is an expert in geometric measure theory. He recommended the book as a very nice exposition of some of the material found in Federer's "Geometric Measure Theory" as well as other material. I found the book to be beautifully designed to help the reader learn its contents. There was enough between the lines so that one needed to WORK through the book, but in contrast to parts of Federer's book, enough detail so that reasonably fast progress could be made. Unfortunately, I was interupted in my race through the book and so I have yet to work through the latter part of the book. But given the large part I did cover and my experience doing that, I am certain to finish the monograph, most likely when I start using functions of bounded variation with any frequency.
There are no explicit exercises. But as already alluded to above, there are implicit exercises that are encountered in working through the book. I found that the lack of separate exercises is actually not bad at all since the implicit exercises encountered are automatically motivated by their necessity for the understanding of the text - and are therefore relevant!
A prerequisite for the book is a course in analysis that includes measure theory and integration as well as an exposure to elementary functional analysis. The functional analysis is not actually necessary, but the added maturity that such an exposure would impart would be useful.
Very briefly, the contents via the 6 chapter titles are 1) General Measure Theory, 2) Hausdorff Measure, 3) Area and Coarea Formulas, 4) Sobolev Functions, 5) BV Functions and Sets of Finite Perimeter, and 6) Differentiability and Approximation by C^1 Functions.
I found the contents very interesting ... quoting the authors "... we packed into these notes all sorts of interesting topics that working mathematical analysts need to know, but are mostly not taught." And indeed this was the case in my experience ... both the "interesting" part and the "not taught" part.
I am disappointed in the price, but if any book is worth it, this one certainly is.
Average customer rating:
- A great book for mathematicians and the best I know for engineers, economists and physicists
- A Classic
- Excellent introductory book on functional analysis
- Good
- Makes you actually WANT to study analysis!
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Introductory Functional Analysis with Applications
Erwin Kreyszig
Manufacturer: Wiley
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Elements of the Theory of Functions and Functional Analysis
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Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
ASIN: 0471504599 |
Book Description
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.
Customer Reviews:
A great book for mathematicians and the best I know for engineers, economists and physicists.......2007-01-24
There is no doubt that Professor Kreysig has written one of the best books of functional analysis. The advantages of this book are the absence of advanced pre-requisites (one has only to know basic concepts of calculus and linear algebra), easy of explanation ( the proofs of the book are really clear), the selection of subjects (one may find in this book more specific topics such as the relation between banach algebras and spectral theory and spectral theory of unbounded operators but also applications such as numerical methods which are very useful for engineers) and the structure of the book (divided in sections with many interesting exercises at the end of each section). Finally, I believe that the main advantage of the book is that, if are not a mathematician, it provides you the motivation to learn these some what abstract concepts.
This book may be used as the main reference in the classroom or also for self-study. In fact, this book is particularly suitable for engineers, economists and physicists. In fact, the last chapter of this book presents an introduction to quantum physics.
A Classic.......2006-12-14
This was my textbook for a graduate course in functional analysis, and it is called "classic" by many professors. Don't be fooled by the title of the book: "Introductory" simply means the author assumes you have not seen the subject before, and it is by no means an easy subject. However, the exposition is extremely clear. Kreyszig saved me on numerous occasions as my companion on a treacherous journey through graduate functional analysis.
This book does what few math textbooks do, though all of them should do. Rather than assail you with theorem, proof, theorem, proof, Kreyszig first tells you what he is about to show you, then explains the motivation -- i.e., why we need the following theorem. Then, once outlined, properly motivated, and placed in context, he delivers the theorem and its proof. Furthermore, Kreyszig explicitly spells out what other texts might assume you will "read between the lines", explaining why and how we are able to take each step forward during a proof.
The problems in the book are also good. They are at a level such that you can attempt them and solve them on your own, while at the same time they give you the hands-on experience you need in order to gain a deeper understanding of the principles at hand. They serve as a great confidence-builder before you venture onward and attempt harder problems (for example, in other texts or in research).
As a final treat for physicists, the last chapter takes the mathematics you've learned throughout the book and applies it in an introduction to quantum mechanics. My only gripe with this final chapter (and indeed my only -- minor -- complaint for the entire book) is that most of the interesting results of quantum mechanics arise not from the book's exposition, but as problems for the reader to work out. Of course, if you want to learn quantum mechanics, this isn't the book to begin with but rather a very nice mathematical supplement.
I highly recommend this book to anyone wanting to learn functional analysis.
Excellent introductory book on functional analysis.......2006-06-16
This book is excellent for so many reasons. The book is self-contained; it is much more accessible than a number of other books. The writing is very clear, occasional use of diagrams is very helpful. Proofs are very easy to follow, and the author gives you a sense of the big picture of the subject before you get to the proof, keeping the reader motivated in a subject that can often seem abstract and boring. The typesetting and layout of the book are also unusually well-executed for a mathematics book: definitions are easy to spot, and the material is presented clearly on the page. The book as a whole is exceptionally well-organized, making it easy to skip around, and making this book an outstanding reference.
One of the best aspects of this book are the examples; the text is rich in examples, especially in the beginning. This aspect drops off a little as you progress in the book, which was honestly a little bit disappointing, since if anything I think it should be the other way around.
The exercises are not particularly difficult, but are appropriate to the level of the book--they will be difficult for people with less background in analysis. Some of them are very easy, others are tedious and/or technical but not particularly deep. I did not work exercises in the advanced chapters as much as the easier chapters though so I can't say about them.
I think some of the more critical reviewers are ignoring the title and audience of this book: this is an introductory book, designed to make the subject accessible at a lower level. For that role, it is simply amazing. Any criticism of this book needs to take this into account--it is not an advanced graduate-level text and should not be evaluated as such.
Good.......2006-01-16
This book is especially good for those who are not mathematicians, and just need some knowledge of functional analysis for computation or application of rigorous theory. This book is well organized in the sense that the shortest path is easily identified for what we want to learn out of this book. I would strongly recommend.
Makes you actually WANT to study analysis!.......2005-12-23
Functional analysis is the branch of mathematics concerned with the study of spaces of functions. It has its historical roots in the study of transformations, such as the Fourier transform, and in the study of differential and integral equations. This usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function. Most textbooks claiming to be introductions to this subject are just one proof after another without a clue as to WHY you would want to study this stuff in the first place. Mr. Kreyszig's book is a welcome addition to the family of textbooks that claim to be introductions to the subject because the material is explained in an accessible fashion alongside applications to the material. So YES as one reviewer put it, this book smells like an engineer's text, but to this reader that is a good thing because I get a feel for how to use the information thus motivating me for further study. I particularly liked the sections applying Banach's Fixed Point Theorem to the solution of differential equations and linear equations. As for the suggestions of other reviewers to reject this book in favor of Rudin's, I think that is a bad suggestion for someone other than a graduate student of pure mathematics. Rudin does a great job of explaining all of the theory, but I think that this book is better at providing motivations for the study of functional analysis through the demonstration of applications. Eventually, you should probably read both books.
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Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications)
V.L. Kocic , and
G. Ladas
Manufacturer: Springer
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ASIN: 079232286X |
Book Description
This volume presents a systematic study of the global behaviour of solutions of nonlinear scalar difference equations of order greater than one. Of particular interest are aspects such as global asymptotic stability, periodicity, permanence and persistence, and also semicycles of solutions. As well as exposing the reader to the very frontiers of the subject, important open problems are also formulated.
The book has six chapters. Chapter 1 presents an introduction to the subject and deals with preliminaries. Chapter 2 considers global stability results. Chapter 3 is devoted to rational recursive structures. Chapter 4 describes various applications. The topic of Chapter 5 is periodic cycles, and Chapter 6 discusses a number of open problems and conjectures involving interesting types of difference equations. Each chapter includes notes and references. The volume concludes with three appendices, a comprehensive bibliography, and name and subject indices.
For graduate students and researchers whose work involves difference and differential equations.
Book Description
The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance provides an overview of the theory and practical applications of wavelet transform methods. The author uses several hundred illustrations, some in color, to convey mathematical concepts and the results of applications. The first chapter presents a brief overview of the wavelet transform, including a short history. The remainder of the book is split into two parts: the first part discusses the mathematics of both discrete and continuous wavelet transforms while the second part deals with applications in a variety of subject areas, such as geophysics, medicine, fluid turbulence, engineering testing, speech and sound analysis, image analysis, and data compression. These application chapters make the reader aware of the similarities that exist in the use of wavelet transform analysis across disciplines. A comprehensive list of more than 700 references provides a valuable resource for further study. The book is designed specifically for the applied reader in science, engineering, medicine, finance, or any other of the growing number of application areas. Newcomers to the subject will find an accessible and clear account of the theory of continuous and discrete wavelet transforms, providing a large number of examples of their use across a wide range of disciplines. Readers already acquainted with wavelets can use the book to broaden their perspective.
Customer Reviews:
An excellent and informative book.......2003-09-26
This book provides a comprehensive overview of wavelet transform methodologies and applications. The emphasis is on practical applications which are illustrated with many detailed figures and examples from Science and Engineering. A particular interesting chapter on medical applications is provided. In the introductory chapters, Addison gives a clear account of the theory for both continuous and discrete wavelet transform and associated post-processing techniques. Unlike many of the other books in this area, Addison communicates the concepts with a level of detail, sufficient for the applied engineer and scientist, but without becoming bogged down in a fog of mathematical gymnastics (a feature of many of the books in this area). A welcome addition to the growing number of books on this important signal analysis technique.
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Interpolation of Operators, Volume 129 (Pure and Applied Mathematics)
Colin Bennett , and
Robert C. Sharpley
Manufacturer: Academic Press
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ASIN: 0120887304 |
Book Description
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.
The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.
Book Description
The fourth and fifth volumes of this extensive multivolume project Integrals and Series are devoted to tables of Laplace transforms. In these companion volumes the authors have collected data scattered throughout the literature, and have augmented this material with many unpublished results obtained in their own research. Volume 4 contains tables of direct Laplace transforms, a number of which are expressed in terms of the Meijer G-function. When combined with the table of special cases, these formulae can be used to obtain Laplace transforms of numerous elementary functions of mathematical physics. Volume 5 offers tables of inversion formulae for the Laplace transformation and includes tables of factorization and inversion of various integral transforms.
Book Description
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.
Customer Reviews:
functional data analysis by example.......2002-08-30
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.
functional data analysis by example.......2002-08-30
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 approach that makes the material very accessible to practitioners as well as statisticians and illustrates the variety of problems and that can be handle by this approach.
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Nonlinearity & Functional Analysis: Lectures on Nonlinear Problems in Mathematical Analysis (Pure and Applied Mathematics, a Series of Monographs and Tex)
Melvyn S. Berger
Manufacturer: Academic Press
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ASIN: 0120903504 |
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