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.
Book Description
Duration, Convexity and other Bond Risk Measures offers the most comprehensive coverage of bond risk measures available. Financial expert Frank Fabozzi walks you through every aspect of bond risk measures from the price volatility characteristics of option-free bonds and bonds with embedded options to the proper method for calculating duration and convexity. Whether you're a novice trader or experienced money manager, if you need to understand the interest rate risk of a portfolio Duration, Convexity and other Bond Risk Measures is the only book you'll need.
Customer Reviews:
Good book.......2005-06-11
This a good basic introduction. Also try Interest Rate Risk Modeling: A Fixed Income Valuation Course by Nawalkha et. al, and the website www.fixedincomerisk.com with a free forum and free software download.
Frank's best short story.......2003-10-14
Fabozzi has a lot of intuitive books, but I think this is the best concise book out there that provides a focused discussion on Convexity and Duration. Lucid on all aspects of bond convexity and a very good analysis of option embedded bonds with negative convexity.
Comprehensive review of fundamental concepts........2000-05-25
the book gives the fundamentals of risk management. You can grasp the idea of duration, convexity and other commonly used terms. The book especially tells how you will use the terms, not to derive them. I recommend the book, it is indeed useful
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Fourier Analysis and Convexity (Applied and Numerical Harmonic Analysis)
Manufacturer: Birkhäuser Boston
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ASIN: 0817632638 |
Book Description
Over the course of the last century, the systematic exploration of the relationship between Fourier analysis and other branches of mathematics has lead to important advances in geometry, number theory, and analysis, stimulated in part by Hurwitz’s proof of the isoperimetric inequality using Fourier series.
This unified, self-contained volume is dedicated to Fourier analysis, convex geometry, and related topics. Specific topics covered include:
* the geometric properties of convex bodies
* the study of Radon transforms
* the geometry of numbers
* the study of translational tilings using Fourier analysis
* irregularities in distributions
* Lattice point problems examined in the context of number theory, probability theory, and Fourier analysis
* restriction problems for the Fourier transform
The book presents both a broad overview of Fourier analysis and convexity as well as an intricate look at applications in some specific settings; it will be useful to graduate students and researchers in harmonic analysis, convex geometry, functional analysis, number theory, computer science, and combinatorial analysis. A wide audience will benefit from the careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.
Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch
Book Description
In this volume, Ekeland and Turnbull are mainly concerned with existence theory. They seek to determine whether, when given an optimization problem consisting of minimizing a functional over some feasible set, an optimal solution—a minimizer—may be found.
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Bond Risk Analysis: A Guide to Duration and Convexity
Livingston G. Douglas
Manufacturer: Prentice Hall Trade
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ASIN: 0132210371 |
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Gian-Carlo Rota on Analysis, Convexity, and Probability
Jean Dhombres
Manufacturer: Birkhäuser Boston
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ASIN: 0817642757 |
Book Description
Gian-Carlo Rota was one of those rare mathematicians who made major contributions to several areas of mathematics. Presented in the first part of this volume are reprints of his papers in analysis, which were written at the beginning of his career. These papers on differential equations, operator theory, ergodic theory, and other subjects have a continuing and pervasive influence. Reprints of his papers on convexity and probability theory are presented in the second part of the work. These were written towards the end of his career and contain many ideas that have yet to be fully developed. Comprehensive commentaries are included in every chapter. These survey articles detail work inspired by Rota's papers and also include discussions of many unsolved problems.
As is customary with Rota's writings, the papers included in the volume – some published here for the first time – contain many fresh and unexpected ideas for further research. Thus, this volume will be of interest to both experts and beginners in the above-mentioned fields.
Contributors: J. Dhombres, P.L. Duren, W.N. Everitt, D.A. Klain, J.P.S. Kung, A. Ramsay, M.M. Rao, J. Rovnyak, H.H. Schaefer, B. Schultze, J.T. Schwartz, N. Starr, G. Strang, D.C. Torney, R. Zaharopol, A. Zettl, X.-D. Zhang
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Convexity and Well-Posed Problems (CMS Books in Mathematics)
Roberto Lucchetti
Manufacturer: Springer
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ASIN: 0387287191 |
Book Description
This book deals with the study of convex functions and of their behavior from the point of view of stability with respect to perturbations. Convex functions are considered from the modern point of view that underlines the geometrical aspect: thus a function is defined as convex whenever its graph is a convex set. A primary goal of this book is to study the problems of stability and well-posedness, in the convex case. Stability means that the basic parameters of a minimum problem do not vary much if we slightly change the initial data. On the other hand, well-posedness means that points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of functions and of sets. This approach fits perfectly with the idea of regarding functions as sets. Thus the second part of the book starts with a short, yet rather complete, overview of the so-called hypertopologies, i.e. topologies in the closed subsets of a metric space. While there exist numerous classic texts on the issue of stability, there only exists one book on hypertopologies [Beer 1993]. The current book differs from Beer’s in that it contains a much more condensed explication of hypertopologies and is intended to help those not familiar with hypertopologies learn how to use them in the context of optimization problems.
Book Description
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category.
At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodifferential calculus is required, but these sections can be bypassed with no loss of continuity. The major part of the book should therefore be accessible to graduate students so that it can serve as an introduction to complex analysis in one and several variables. The last sections, however, are written mainly for readers familiar with microlocal analysis.
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.
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Convexity (Oxford Science Publications)
Roger Webster
Manufacturer: Oxford University Press, USA
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A Course in Convexity (Graduate Studies in Mathematics, V. 54)
ASIN: 0198531478 |
Book Description
Convexity provides a wide-ranging introduction for final year undergraduates and graduate students. Convex sets and functions are studied in the Euclidean space IRn, thus allowing an exposition demanding only an elementary knowledge of analysis and linear algebra, and enabling concepts to be motivated through simple geometric examples. The fundemental ideas of convexity are natural and appealing, and does not have to travel far along its path, before meeting significant, aesthetically pleasing results. It develops geometric intuition, and is a showcase for displaying interconnections amongst different parts of mathematics, in addition to have ties with economics, science and engineering. Despite being an active research field, it abounds in unsolved problems having an instant intuitive appeal. One distinctive feature of the book is the diverse applications that it highlights: number theory, geometric extremum problems, combinatorial geometry, linear programming, game theory, polytopes, bodies of constant width, the gamma function, minimax approximation, and linear, classical and matrix inequalities. Several topics make their first appearance in a general introduction to convexity, while a few have not appeared outside research journals. The account has a self-contained treatment of volume, thus permitting a rigorous discussion of mixed volumes, is operimetry and Brunn-Minkowski theory. Full solutions to most of the 241 exercises are provided and detailed suggestions for further reading are given.
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