Convexity : an analytic viewpoint
By: Simon, Barry.
Series: Cambridge tracts in mathematics. / edited by B. Bollobas; v.187.Publisher: New York Cambridge University Press 2011Description: ix, 345p.ISBN: 9781107007314.Subject(s): Mathematical analysis | Convex domainsDDC classification: 516 | Si53c Summary: 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 | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
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Books
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PK Kelkar Library, IIT Kanpur | General Stacks | 516 Si53c (Browse shelf) | Available | A184418 |
Browsing PK Kelkar Library, IIT Kanpur Shelves , Collection code: General Stacks Close shelf browser
| 516 Sh28e Explorations in geometry | 516 SI11G GEOMETRIC VIEWPOINT | 516 SI38G GEOMETRY ANCIENT AND MODERN | 516 Si53c Convexity | 516 Sm5a2 ANALYTIC GEOMETRY | 516 Sm5a2 ANALYTIC GEOMETRY | 516 So55a Analytical geometry of three dimensions |
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.
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