登入選單
返回Google圖書搜尋
Convexity
Barry Simon
其他書名
An Analytic Viewpoint
出版Cambridge University Press, 2011-05-19
主題Mathematics / Algebra / AbstractMathematics / CalculusScience / Physics / Mathematical & Computational
ISBN11394975969781139497596
URLhttp://books.google.com.hk/books?id=xWCs0lWGxjkC&hl=&source=gbs_api
EBookSAMPLE
註釋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.