Compact Convex Sets And Boundary Integrals

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Compact Convex Sets And Boundary Integrals

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Author : Erik Magnus Alfsen
language : en
Publisher:
Release Date : 195?

Compact Convex Sets And Boundary Integrals written by Erik Magnus Alfsen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 195? with Boundary value problems categories.

Compact Convex Sets And Boundary Integrals

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Author : Erik M. Alfsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Compact Convex Sets And Boundary Integrals written by Erik M. Alfsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop -de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and tech nically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominated extension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral for mulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applica tions, in particular to operator theory and function algebras.

Compact Convex Sets And Boundary Integrals

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Author : Erik Magnus Alfsen (mathématicien).)
language : en
Publisher:
Release Date :

Compact Convex Sets And Boundary Integrals written by Erik Magnus Alfsen (mathématicien).) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Integral Representation Theory

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Author : Jaroslav Lukeš
language : en
Publisher: Walter de Gruyter
Release Date : 2010

Integral Representation Theory written by Jaroslav Lukeš and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

"This monograph provides an extensive and largely self-contained exposition of integral representation theory with emphasis on applications in mathematical analysis. It is focused on the Choquet theory of function spaces, function cones and compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time." --Book Jacket.

Introduction To Operator Algebras

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Author : Bing-Ren Li
language : en
Publisher: World Scientific
Release Date : 1992

Introduction To Operator Algebras written by Bing-Ren Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book is an introductory text on one of the most important fields of Mathematics, the theory of operator algebras. It offers a readable exposition of the basic concepts, techniques, structures and important results of operator algebras. Written in a self-contained manner, with an emphasis on understanding, it serves as an ideal text for graduate students.

Geometric Aspects Of Convex Sets With The Radon Nikodym Property

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Author : R. D. Bourgin
language : en
Publisher: Springer
Release Date : 2006-11-15

Geometric Aspects Of Convex Sets With The Radon Nikodym Property written by R. D. Bourgin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Integral Operators In The Theory Of Linear Partial Differential Equations

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Author : Stefan Bergman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Integral Operators In The Theory Of Linear Partial Differential Equations written by Stefan Bergman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.

Theory And Applications Of Models Of Computation

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Author : Jin-Yi Cai
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11

Theory And Applications Of Models Of Computation written by Jin-Yi Cai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Computers categories.

TAMC 2006 was the third conference in the series. The previous two meetings were held May 17–19, 2004 in Beijing, and May 17–20, 2005 in Kunming

Theory Of Linear Operations

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Author : S. Banach
language : en
Publisher: Elsevier
Release Date : 1987-03-01

Theory Of Linear Operations written by S. Banach and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-01 with Computers categories.

This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

Functional Analysis And Operator Algebras

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Author : Kenneth R. Davidson
language : en
Publisher: Springer Nature
Release Date : 2025-05-11

Functional Analysis And Operator Algebras written by Kenneth R. Davidson and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-11 with Mathematics categories.

This book offers a comprehensive introduction to various aspects of functional analysis and operator algebras. In Part I, readers will find the foundational material suitable for a one-semester course on functional analysis and linear operators. Additionally, Part I includes enrichment topics that provide flexibility for instructors. Part II covers the fundamentals of Banach algebras and C*-algebras, followed by more advanced material on C* and von Neumann algebras. This section is suitable for use in graduate courses, with instructors having the option to select specific topics. Part III explores a range of important topics in operator theory and operator algebras. These include $H^p$ spaces, isometries and Toeplitz operators, nest algebras, dilation theory, applications to various classes of nonself-adjoint operator algebras, and noncommutative convexity and Choquet theory. This material is suitable for graduate courses and learning seminars, offering instructors flexibility in selecting topics.