Compact convex sets and boundary integrals.

Alfsen, Erik M.:

ISBN 10: 3540050906 / ISBN 13: 9783540050902

Published by Berlin, 1971

210 S. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. R-16732 3540050906 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2480117

Synopsis:

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.

Bibliographic Details

Title: Compact convex sets and boundary integrals.
Publisher: Berlin
Publication Date: 1971
Binding: Hardcover