Compact Convex Sets and Boundary Integrals: 57 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

Book Details

• Publisher: Springer

• Author: Erik M. Alfsen

• Language: English

• Edition: Softcover reprint of the original 1st Edition (1971)

• ISBN: 9783642650116

• Pages: 212

• Binding: Paperback

• Dimensions: 9.0 x 6.0 x 0.5 inches

About The Book

Convex Sets and Functions in Infinite Dimensions by Erik M. Alfsen is a pivotal text in the field of functional analysis, focusing on the theory of infinite-dimensional convex sets. While convexity arguments have long played a key role in functional analysis, it wasn’t until the integral representation theorems of Choquet and Bishop-de Leeuw that a comprehensive theory of infinite-dimensional convex sets emerged. This work marks a new era in convexity theory, and Alfsen’s book offers a unified approach to understanding this groundbreaking development.

The book delves into key concepts such as the interplay between compact convex sets and their associated spaces, duality between faces of these sets and ideals, and the important problems regarding dominated-extension for continuous affine functions. Alfsen also explores direct convex sum decompositions into faces, and integral formulas that generalize these decompositions.

By integrating these theoretical results with applications in operator theory, function algebras, and ergodic theory, this text stands as an essential reference for anyone interested in the geometric and abstract aspects of convexity. The methods introduced in this book have become foundational, offering a bridge between abstract theory and practical applications across several fields, including potential theory, probability, and group representations.

Ideal for graduate students and researchers, Convex Sets and Functions in Infinite Dimensions is an indispensable resource for anyone working in the area of functional analysis and its diverse applications.