Integral Representation Theory Applications to Convexity, Banach Spaces and Potential Theory

This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, su...

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Bibliographic Details
Main Authors: Lukes, Jaroslav, Malý, Jan, Netuka, Ivan, Spurný, Jirí
Format: eBook Book
Language:English
Published: Germany De Gruyter 2009
Walter de Gruyter
Walter de Gruyter GmbH
Edition:1
Series:De Gruyter Studies in Mathematics
Subjects:
Banach spaces
Convex Analysis
Convex domains
Dirichlet Problem
Dirichletsches Problem
Functional Analysis
Funktionalanalysis
Integral representations
MATHEMATICS
MATHEMATICS / Functional Analysis
MATHEMATICS / General
MATHEMATICS / Mathematical Analysis
Mathematics. Analysis
MATHEMATICS / Differential Equations / General
Partial Differential Equation
Partielle Differentialgleichung
Potential Theory
Potential theory (Mathematics)
Potentialtheorie
Dirichlet Problem
Funktionalanalysis
Convex Analysis
Partielle Differentialgleichung
Functional Analysis
Potential Theory
Partial Differential Equation
Potentialtheorie
Dirichletsches Problem
ISBN:9783110203219, 3110203219, 3110203200, 9783110203202
Online Access:Get full text
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Summary:This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to 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. The text is self-contained and covers a wide range of applications. From the contents: * Geometry of convex sets * Choquet theory of function spaces * Affine functions on compact convex sets * Perfect classes of functions and representation of affine functions * Simplicial function spaces * Choquet's theory of function cones * Topologies on boundaries * Several results on function spaces and compact convex sets * Continuous and measurable selectors * Construction of function spaces * Function spaces in potential theory and Dirichlet problem * Applications
Bibliography:Other authors: Jan Malý, Ivan Netuka, Jiří Spurný
Includes bibliography (p. [669]-694) and index
ISBN:9783110203219
3110203219
3110203200
9783110203202
DOI:10.1515/9783110203219