Integral representation theory : applications to convexity, banach spaces and potential theory / Jaroslav Lukes ... [et al.].

Format:

Book

Contributor:

Lukeš, Jaroslav, 1940-

Series:

De Gruyter studies in mathematics ; 35.

De Gruyter studies in mathematics ; 35

Language:

English

Subjects (All):

Functional analysis.

Convex domains.

Banach spaces.

Potential theory (Mathematics).

Integral representations.

Physical Description:

1 online resource (731 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : Walter de Gruyter, c2010.

Language Note:

English

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

Contents:

Frontmatter

Contents

1 Prologue

2 Compact convex sets

3 Choquet theory of function spaces

4 Affine functions on compact convex sets

5 Perfect classes of functions and representation of affine functions

6 Simplicial function spaces

7 Choquet theory of function cones

8 Choquet-like sets

9 Topologies on boundaries

10 Deeper results on function spaces and compact convex sets

11 Continuous and measurable selectors

12 Constructions of function spaces

13 Function spaces in potential theory and the Dirichlet problem

14 Applications

Backmatter

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612714368

9781282714366

1282714368

9783110203219

3110203219

OCLC:

651048124