Convexity: An Analytic Viewpoint (Cambridge Tracts in Mathematics, Series Number 187) by Barry Simon (PDF)

Description

Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner’s theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject’s history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.

User’s Reviews

Editorial Reviews: Review “Simon’s monograph is a valuable addition to the literature on convexity that will inspire many minds enchanted by the beauty and power of the cornerstone of functional analysis.” S. Kutateladze, Mathematical Reviews Book Description A comprehensive look at convexity and its mathematical ramifications. About the Author Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology. Read more

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