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Convexity: An Analytic Viewpoint

Simon, Barry (2011) Convexity: An Analytic Viewpoint. Cambridge Tracts in Mathematics. No.187. Cambridge University Press , Cambridge. ISBN 9781107007314. http://resolver.caltech.edu/CaltechAUTHORS:20180808-075325457

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Abstract

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.


Item Type:Book
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/CBO9780511910135DOIBook Publisher
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2011 Cambridge University Press.
Record Number:CaltechAUTHORS:20180808-075325457
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180808-075325457
Official Citation:Simon, B. (2011). Convexity: An Analytic Viewpoint (Cambridge Tracts in Mathematics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511910135
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88638
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Aug 2018 16:07
Last Modified:08 Aug 2018 16:07

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