TY - BOOK ID - 77740270 TI - Integral Representation Theory AU - Lukeš, Jaroslav, AU - Maly, Jan AU - Netuka, Ivan AU - Spurný, Jirí PY - 2009 SN - 1282714368 9786612714368 3110203219 9783110203219 9783110203202 3110203200 PB - Berlin Boston DB - UniCat KW - Functional analysis. KW - Convex domains. KW - Banach spaces. KW - Potential theory (Mathematics) KW - Integral representations. KW - Representations, Integral KW - Algebraic number theory KW - Crystallography, Mathematical KW - Representations of groups KW - Green's operators KW - Green's theorem KW - Potential functions (Mathematics) KW - Potential, Theory of KW - Mathematical analysis KW - Mechanics KW - Functions of complex variables KW - Generalized spaces KW - Topology KW - Convex regions KW - Convexity KW - Calculus of variations KW - Convex geometry KW - Point set theory KW - Functional calculus KW - Functional equations KW - Integral equations KW - Convex Analysis. KW - Dirichlet Problem. KW - Functional Analysis. KW - Partial Differential Equation. KW - Potential Theory. KW - Functional analysis KW - Convex domains KW - Banach spaces KW - Integral representations UR - https://www.unicat.be/uniCat?func=search&query=sysid:77740270 AB - 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 ER -