000			01627 a2200229 4500
005			20190603155502.0
008			190530b xxu||||| |||| 00| 0 eng d
020			_a9781107007314
040			_cIIT Kanpur
041			_aeng
082			_a516 _bSi53c
100			_aSimon, Barry
245			_aConvexity _ban analytic viewpoint _cBarry Simon
260			_bCambridge University Press _c2011 _aNew York
300			_aix, 345p
440			_aCambridge tracts in mathematics
490			_a / edited by B. Bollobas; v.187
520			_aConvexity 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.
650			_aMathematical analysis
650			_aConvex domains
942			_cBK
999			_c560278 _d560278