Convexity: an analytic viewpoint
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...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Schriftenreihe: | Cambridge tracts in mathematics
187 |
| Links: | https://doi.org/10.1017/CBO9780511910135 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (ix, 345 Seiten) |
| ISBN: | 9780511910135 |
Internformat
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| spelling | Simon, Barry 1946- Convexity an analytic viewpoint Barry Simon Cambridge Cambridge University Press 2011 1 Online-Ressource (ix, 345 Seiten) txt c cr Cambridge tracts in mathematics 187 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. Erscheint auch als Druck-Ausgabe 9781107007314 Erscheint auch als Druck-Ausgabe 9781107471368 |
| spellingShingle | Simon, Barry 1946- Convexity an analytic viewpoint |
| title | Convexity an analytic viewpoint |
| title_auth | Convexity an analytic viewpoint |
| title_exact_search | Convexity an analytic viewpoint |
| title_full | Convexity an analytic viewpoint Barry Simon |
| title_fullStr | Convexity an analytic viewpoint Barry Simon |
| title_full_unstemmed | Convexity an analytic viewpoint Barry Simon |
| title_short | Convexity |
| title_sort | convexity an analytic viewpoint |
| title_sub | an analytic viewpoint |
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