Books in Functional analysis

Functional Analysis, Holomorphy and Approximation Theory

1st Edition
Volume 71
April 1, 2000
J.A. Barroso
English
eBook
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New Generalized Functions and Multiplication of Distributions

1st Edition
Volume 84
April 1, 2000
J.F. Colombeau
English
eBook
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This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.

Summability Through Functional Analysis

1st Edition
Volume 85
April 1, 2000
A. Wilansky
English
eBook
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Summability is an extremely fruitful area for the application of functional analysis; this volume could be used as a source for such applications. Those parts of summability which only have ``hard'' (classical) proofs are omitted; the theorems given all have ``soft'' (functional analytic) proofs.

Functional Analysis, Holomorphy and Approximation Theory II

1st Edition
Volume 86
April 1, 2000
G.I. Zapata
English
eBook
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Functional Analysis: Surveys and Recent Results III

1st Edition
Volume 90
April 1, 2000
K.-D. Bierstedt + 1 more
English
eBook
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This volume contains 22 articles on topics of current interest in functional analysis, operator theory and related areas. Some of the papers have connections with complex function theory in one and several variables, probability theory and mathematical physics.Surveys of some areas of recent progress in functional analysis are given and related new results are presented. The topics covered in this volume supplement the discussion of modern functional analysis in the previous Proceedings volumes. Together with the previous volumes, the reader obtains a good impression of many aspects of present-day functional analysis and its applications. Parts of this volume can be used profitably in advanced seminars and courses in functional analysis.

Analytic Sets in Locally Convex Spaces

1st Edition
Volume 89
April 1, 2000
P. Mazet
English
eBook
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Introduction to Hilbert Spaces with Applications

3rd Edition
February 14, 2000
Lokenath Debnath + 1 more
English
Hardback
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eBook
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Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.

Big-Planes, Boundaries and Function Algebras

1st Edition
Volume 172
March 2, 1992
T.V. Tonev
English
eBook
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Treated in this volume are selected topics in analytic &Ggr;-almost-per... functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-per... structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.

Progress in Functional Analysis

1st Edition
Volume 170
January 10, 1992
K.D. Bierstedt + 3 more
English
eBook
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This volume includes a collection of research articles inFunctional Analysis, celebrating the occasion of Manuel Valdivia'ssixtieth birthday. The papers included in the volume are basedon the main lectures presented during the internationalfunctio... analysis meeting held in Peñíscola(Valencia, Spain) in October 1990.During his career, Valdiviahas made contributions to a wide variety of areas of FunctionalAnalysis and his work has had a profound impact. A thoroughappreciation of Valdivia's work is presented in J.Horváth's article. In honor of Valdivia's achievements, this volume presents more than twenty-five papers on topics related to his research(Banach spaces, operator ideals, tensor products, Fréchet,(DF) and (LF) spaces, distribution theory, infinite holomorphyetc.). While the majority of papers are research articles, survey articles are also included. The book covers a broad spectrum of interests in today's Functional Analysis and presents new results by leading specialists in the field.

Interpolation Functors and Interpolation Spaces

1st Edition
Volume 47
March 18, 1991
Yu.A. Brudnyi + 1 more
English
eBook
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The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the results of that solution, as well as drawing heavily on a classic paper by Aronszajn and Gagliardo, which appeared in 1965 but whose real importance was not realized until a decade later. This includes a systematic use of the language, if not the theory, of categories. In this way the book also opens up many new vistas which still have to be explored. This volume is the first of three planned books. Volume II will deal with the complex method, while Volume III will deal with applications.

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