Convexity
An Analytic Viewpoint
1st Edition
Published on 30. May 2011
978-1-139-06618-1 (ISBN)
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.
Reviews / Votes
"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
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 55 Tables, unspecified; 55 Plates, unspecified; 3 Halftones, unspecified; 5 Line drawings, unspecified
File size
1,69 MB
ISBN-13
978-1-139-06618-1 (9781139066181)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
05/2011
Cambridge University Press
€117.70
Shipment within 15-20 days
Person
Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology.
Content
Preface; 1. Convex functions and sets; 2. Orlicz spaces; 3. Gauges and locally convex spaces; 4. Separation theorems; 5. Duality: dual topologies, bipolar sets, and Legendre transforms; 6. Monotone and convex matrix functions; 7. Loewner's theorem: a first proof; 8. Extreme points and the Krein-Milman theorem; 9. The strong Krein-Milman theorem; 10. Choquet theory: existence; 11. Choquet theory: uniqueness; 12. Complex interpolation; 13. The Brunn-Minkowski inequalities and log concave functions; 14. Rearrangement inequalities: a) Brascamp-Lieb-Luttinger inequalities; 15. Rearrangement inequalities: b) Majorization; 16. The relative entropy; 17. Notes; References; Author index; Subject index.
