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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.

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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
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URLURL TypeDescription Publisher
Simon, Barry0000-0003-2561-8539
Additional Information:© 2011 Cambridge University Press.
Series Name:Cambridge Tracts in Mathematics
Issue or Number:187
Record Number:CaltechAUTHORS:20180808-075325457
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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
Deposited By: Tony Diaz
Deposited On:08 Aug 2018 16:07
Last Modified:16 Nov 2021 00:28

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