Convexity

An Analytic Viewpoint

By Barry Simon

2011

First Published

356

Number of Pages

10H48M

Audio Length

Part of Series

Cambridge Tracts in Mathematics book cover 1

Cambridge Tracts in Mathematics

Series · 61 books

By H. Halberstam, P. B. Kirkpatrick, James C. Robinson, and more

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 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.

Author

Barry Simon

Author · 2 books

Barry Simon is an eminent American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics (Emeritus) at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics (particularly Schrödinger operators), including the connections to atomic and molecular physics. He has authored more than 300 publications on mathematics and physics. More particularly, his work has focused on broad areas of mathematical physics and analysis covering: quantum field theory, statistical mechanics, Brownian motion, random matrix theory, general nonrelativistic quantum mechanics (including N-body systems and resonances), nonrelativistic quantum mechanics in electric and magnetic fields, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators, orthogonal polynomials, and non-selfadjoint spectral theory. Dr. Simon is a fellow of the American Mathematical Society (2012), a winner of the Henri Poincaré Prize (2012), a winner of the János Bolyai International Mathematical Prize (2015), a winner of the 2016 Steele Prize for Lifetime Achievement, and a winner of the Dannie Heineman Prize for Mathematical Physics (2018).