Integral representation theory applications to convexity, Banach spaces and potential theory - Lukeš, Jaroslav 1940-; Malý, Jan 1955-; Netuka, Ivan; Spurný, Jiří (De Gruyter, 2010)
Includes bibliographical references (pages 669-694) and index
Compact 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 theory of function cones -- Choquet-like sets -- Topologies on boundaries -- Deeper results on function spaces and compact convex sets -- Continuous and measurable selectors -- Constructions of function spaces -- Function spaces in potential theory and the Dirichlet problem -- Applications
This ambitious and substantial monograph, written by prominent experts in the field, presents the state of the art of convexity, with an emphasis on the interplay between convex analysis and potential theory; more particularly, between Choquet theory and the Dirichlet problem. The book is unique and self-contained, and it covers a wide range of applications which will appeal to many readers
Keywords: MATHEMATICS / Functional Analysis; Banach-Raum; Choquet-Theorie; Integraldarstellung; Konvexe Menge; Potenzialtheorie; Banach spaces; Convex domains; Functional analysis; Integral representations; Potential theory (Mathematics)