Functional Analysis

Book Description

This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Customer Reviews:

As a reference, this is nice, but as a book for first-time learners..........2007-08-28

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

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

Outstanding.......2007-05-30

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

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

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

Modern topics in math........2003-04-05

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

The Bible on Distributions.......1999-06-15

No other book covers the elements of distributions and the fourier transform quite like Rudin's Functional Analysis. This is a must for every budding PDE-er!

Uno de los mejores en Análisis Funcional.......1998-02-05

De los excelentes textos en Análisis Funcional que existen en el mercado, éste es de los mejores. Tiene una excelente presentación de la Teoría de Distribuciones, en los capítulos 6, 7 y 8. La teoría espectral como se trata aca es magnifica. Tambien tiene un desarrollo muy completo sobre espacios vectoriales topológicos. Termina con una reseña bibliográfica muy completa.

Optimization by Vector Space Methods (Series in Decision and Control)

Average customer rating:

Elegant and astonishing
A Good Book but Seriously Overpriced
This is a true classic
Simply the perfect math book
Thank You Dr. Luenberger

Optimization by Vector Space Methods (Series in Decision and Control)
David G. Luenberger
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Paperback

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Linear and Nonlinear Programming, Second Edition
Convex Analysis (Princeton Landmarks in Mathematics and Physics)
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ASIN: 047118117X

Book Description

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Customer Reviews:

Elegant and astonishing.......2006-03-17

Professor Luenberger unites many areas of optimization using a few principles from functional analysis. The explanations are clear and the proofs are compact and elegant. This book is your tool for understanding the deep connection between linear programming, convex optimization, game theory, optimal control and series approximation (e.g. Fourier series).

Luenberger's book has over 1300 citations as of March 2006. In my opinion, the material in this book is essential for any graduate student or professional who intends to contribute to the literature in optimization or optimal control.

A Good Book but Seriously Overpriced.......2005-01-15

The exposition is pretty clear and the book has a good number of worked non-trivial examples. At $40 this would be a great book, but $100 for a PAPERBACK book written 30 years ago is a bit ridiculous. The first 1/4 of the book is also a (very) basic introduction to functional analysis which, if you have had any contact with this subject before, you will probably skip making the book quite short.

This is a true classic.......2004-12-18

This book is a timeless classic, filled with extraordinarily powerful mathematics and applicable to just about every serious subject area. Luenberger did a masterful job of writing a book that will "unravel the spaghetti" seen in most other books. The visual perspectives he provides to seemingly abstract ideas are the key.

Simply the perfect math book.......2003-07-04

Optimization by Vector Space Methods, by David Luenberger, is one of the finest math texts I have ever read, and I've read hundreds. Many years ago this book sparked my interest in optimization and convinced me that the abstract mathematics I had been immersed in actually would be applicable to real problems. Since then, Luenberger's book has inspired several of my graduate students. I merely lent them my copy, and Luenberger did the rest; he drew them in by carefully laying the foundation for an elegant theory, with just the right mix of formalism and intuition, and opened their eyes to the beauty and practicality of abstract mathematics. Anyone with an interest in higher-level mathematics (beyond multi-variable calculus, say) would benefit from exposure to this finely-crafted book. I daresay, the rampant math anxiety that is so prevalent in the West would be substantially reduced if more authors would take such meticulous care in presenting their material.

The format of Luenberger's book is also extremely appealing in a way that I cannot quite put my finger on. The typography and illustrations are inherently crisp and inviting; they draw you in. There is nothing at all superfluous or gratuitous in this book. It is utterly to-the-point, methodical, and above all, clear. The techniques are developed starting from an elementary treatment of vector spaces, then proceeding on to Banach spaces and Hilbert spaces. Along the way, Luenberger introduces convexity, cones, basic topology, random variables, minimum-variance estimators, and least squares, among many other things. There is a recurring theme of duality, which can be used in a way analogous to the inner product of a Hilbert space. In particular, the familiar projection theorems of Hilbert spaces can be echoed in simpler normed linear spaces using duality, which Luenberger motivates and covers beautifully.

The book also covers some of the standard fare of functional analysis, such as the Han-Banach theorem, strong and weak convergence, and the Banach inverse theorem. However, Luenberger never wanders too far off into abstract nonsense; around every corner lay tantalizing application of these ideas to optimization. Luenberger first explores optimization of functionals then covers constrained optimization, which builds upon concepts such as positive cones and Lagrange multipliers. The optimization methods themselves have endless applications in fields such as computer vision, computer graphics, economics, and physics. Indeed, the list is effectively endless as optimization techniques pervade math and science.

I'm certain that the appeal of this book is helped immeasurably by the inherent beauty of the subject matter. Hilbert-space methods are lovely in themselves--they possess a structure that engages one's geometric intuition while at the same time admitting convenient algebraic properties. Once you are in the habit of phrasing problems in abstract settings such as Hilbert spaces, it forever changes how you look at things; you cannot help but look past the clutter to the essence of a problem (or, at least try very hard to do so). While this material is not nearly as abstract as, say, category theory, it nevertheless hits a high point in mathematics--a point more people ought to experience.

If you've had some exposure to optimization methods, or need to apply them in the context of computer vision, graphics, or finance, to mention just a few areas, then I urge you to take a look at Luenberger's fine book. It too hits a high point in clarity of mathematical writing. Combine beautiful theory with endless applications and lucid writing, and you have a winner of a book.

Thank You Dr. Luenberger.......2002-10-15

I owe Dr Luenberger a million thanks for writing this book. As his student, I think he is the master of putting complex issues in simple words. Your faithful student..Jayanth Krishnan

Essential Topology (Springer Undergraduate Mathematics Series)

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A pleasure to read

Essential Topology (Springer Undergraduate Mathematics Series)
Martin D. Crossley
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Topological Invariants of Stratified Spaces (Springer Monographs in Mathematics)
A Topological Picturebook

ASIN: 1852337826

Book Description

Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the University of Wales Swansea, it begins with a discussion of continuity and, by way of many examples, leads to the celebrated "Hairy Ball theorem" and on to homotopy and homology: the cornerstones of contemporary algebraic topology.

While containing all the key results of basic topology, Essential Topology never allows itself to get mired in details. Instead, the focus throughout is on providing interesting examples that clarify the ideas and motivate the student, reflecting the fact that these are often the key examples behind current research.

With chapters on:

continuity and topological spaces
deconstructionist topology
the Euler number
homotopy groups including the fundamental group
simplicial and singular homology, and
fibre bundles

Essential Topology contains enough material for two semester-long courses, and offers a one-stop-shop for undergraduate-level topology, leaving students motivated for postgraduate study in the field, and well-prepared for it.

Customer Reviews:

A pleasure to read.......2007-05-15

I have a major in math, many years ago. I have moved into economics, but miss the elegance of math, hence I decided to revisit some old topics, and started with topology. As a student we used lecture notes and no real textbook, so my choice now was this textbook. It is a pure pleasure to read. I wish we had used it as a text book when I studied.

The topics are well motivated. Crossley does a good job in explaining why we should care about these particular lemmas and theorems. The proofs are usually elegant. I find the estetic pleasures a good math book should provide.

Topological Vector Spaces, Distributions and Kernels

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Topological Vector Spaces, Distributions and Kernels
Francois Treves
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486453529

Book Description

This text for upper-level undergraduates and graduate students focuses on key notions and results in functional analysis. Extending beyond the boundaries of Hilbert and Banach space theory, it explores aspects of analysis relevant to the solution of partial differential equations. It features basic classical results, plus 390 exercises. 1967 edition.

An Introduction to Frames and Riesz Bases

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A new tool!

An Introduction to Frames and Riesz Bases
Ole Christensen
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817642951

Book Description

The theory for frames and bases has developed rapidly in recent years because of its role as a mathematical tool in signal and image processing. In this self-contained work, frames and Riesz bases are presented from a functional analytic point of view, emphasizing their mathematical properties. This is the first comprehensive book to focus on the general properties and interplay of frames and Riesz bases, and thus fills a gap in the literature.

Key features:

* Basic results presented in an accessible way for both pure and applied mathematicians

* Extensive exercises make the work suitable as a textbook for use in graduate courses

* Full proofs included in introductory chapters; only basic knowledge of functional analysis required

* Explicit constructions of frames with applications and connections to time-frequency analysis, wavelets, and nonharmonic Fourier series

* Selected research topics presented with recommendations for more advanced topics and further reading

* Open problems to stimulate further research

An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference.

Customer Reviews:

A new tool!.......2003-02-12

The subject of the book is a new tool in math, with a host of exciting applications. Of course, the subject has roots in classical ideas from harmonic analysis. But the book covers an explosive and exciting variety of developments since roughly 1990, and it is presented in the form of a graduate text. The basic idea begins with linear algebra, and progresses to expansions in function spaces, and multiresolutions. It will be useful to anyone who wants to learn from scratch about the underlying principles, the new results, and the applications. It is well written. A student of mine picked it up accidentally from my desk, and couldn't put it down. After awhile, he had completely forgotten what he came to see me about. It could have been some of the applications, such as antenna theory, wavelets, time-frequency analysis, uses in Radar, speech processing...

Topological Vector Spaces (Cambridge Tracts in Mathematics)

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Topological Vector Spaces (Cambridge Tracts in Mathematics)
Robertson
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

Mathematical Analysis | Mathematics | Science | Subjects | Books

Topological Vector Spaces (Pure and Applied Mathematics)

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Topological Vector Spaces (Pure and Applied Mathematics)
Lawrence Narici , and Edward Beckenstein
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 0824773152

Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity

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It is one clear exposition of very much subjects
I paid Full Price and don't regret it!
A classic text.

Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity
Claude Berge
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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Infinite Dimensional Analysis: A Hitchhiker's Guide
Recursive Macroeconomic Theory, 2nd Edition
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Econometrics
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ASIN: 0486696537

Book Description

Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.

Customer Reviews:

It is one clear exposition of very much subjects.......2005-11-15

To me, this book has the following questions:
- The definition of the entities that appear in the theorems are not precisely defined, what obliges to extract from the proof of very much theorems the exact meaning of some symbols.
- In the proofs there are very much steps thar are 'giant steps'. Usually the author don't reference the theorems and inequalities used in the proofs.
- Also, some symbols coincide, what obliges to extract from the reasoning the exact meaning of few symbols. For example, -G may mean the complement of the set G, or the symmetric of the set G in one numerical space.
However, the book has very much good aspects, like:
- It covers with some detail one great quantity of subjects in only 263 pages, like topological questions, multi-valued mappings, semi-continuity, convexity, symplexes, extremum problems, and very much more. The subjects usually are very interesting and useful.
- The definitions of the main entities analyzed in each paragraph are easy and intuitive.
- The examples are very well chosen, and present very well the problems to study.
- The book is well organized.

I paid Full Price and don't regret it!.......2001-08-05

Although this is so much better than the other Dover book by R. Vaidyanathaswamy, I can't say that it is the best topology text that I have read or the best reference, but it covers topics from Banach spaces to functional topology in a pretty readable manner and it is fairly inexpensive!

A classic text........1999-04-25

Claude Berge's Topological Spaces is a classic text that deserves to be in the libraries of all mathematical economists. It contains many of the fundamental underpinnings of modern mathematical economics. This book has been long out of print and its reprinting by Dover is very welcome. Readers who find this book of interest should also look at Dover's edition of Samuel Karlin's two volume book on mathematical programming and games that has been reprinted as a single volume.

Topological Vector Spaces (Graduate Texts in Mathematics/3)

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a must-to-read book

Topological Vector Spaces (Graduate Texts in Mathematics/3)
H.H. Schaefer , and Helmut H. Schaefer
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387987266

Book Description

This book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is mainly addressed to those readers who have attained and wish to get beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises. These exercises are devoted to further results and supplements, in particular, to examples and counter-examples. Hints have been given where it seemed appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras.

Customer Reviews:

a must-to-read book.......2000-03-26

If you major in mathematical economics, you come across this book again and again. This book includes topological vector spaces and locally convex spaces. Mathematical economists have to master these topics.This book will be a great help for not only mathematicians but economists. Proofs are not hard to follow

Topological Spaces Including a Treatment of Multi-Valued Funcitons, Vector Spaces, and Convexity

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Topological Spaces Including a Treatment of Multi-Valued Funcitons, Vector Spaces, and Convexity

Manufacturer: Macmillan
ProductGroup: Book
Binding: Hardcover
ASIN: B000AUOCIG

Product Description

Hardcover 1963 1st edition of English translation of Espaces Topologiques, fonctions, multivoques by the same author, published by Dunod, Paris, 1959.

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