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Convexity = an analytic viewpoint /

Simon, Barry, (1946-)

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Convexity = an analytic viewpoint /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Convexity/ Barry Simon.
其他題名:	an analytic viewpoint /
作者:	Simon, Barry,
出版者:	Cambridge :Cambridge University Press, : 2011.,
面頁冊數:	ix, 345 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Convex functions and sets -- Orlicz spaces -- Gauges and locally convex spaces -- Separation theorems -- Duality : dual topologies, bipolar sets, and Legendre transforms -- Monotone and convex matrix functions -- Loewner's theorem : a first proof -- Extreme points and the Krein-Milman theorem -- The strong Krein-Milman theorem -- Choquet theory : existence -- Choquet theory : uniqueness -- Complex interpolation -- The Brunn-Minkowski inequalities and log concave functions -- Rearrangement inequalities. Brascamp-Lieb-Luttinger inequalities ; Rearrangement inequalities -- Majorization. The relative entropy.
標題:	Convex domains. -
電子資源:	https://doi.org/10.1017/CBO9780511910135
ISBN:	9780511910135

Convexity = an analytic viewpoint /
Simon, Barry,1946-

Convexityan analytic viewpoint /[electronic resource] :Barry Simon. - Cambridge :Cambridge University Press,2011. - ix, 345 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;187. - Cambridge tracts in mathematics ;187..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Convex functions and sets -- Orlicz spaces -- Gauges and locally convex spaces -- Separation theorems -- Duality : dual topologies, bipolar sets, and Legendre transforms -- Monotone and convex matrix functions -- Loewner's theorem : a first proof -- Extreme points and the Krein-Milman theorem -- The strong Krein-Milman theorem -- Choquet theory : existence -- Choquet theory : uniqueness -- Complex interpolation -- The Brunn-Minkowski inequalities and log concave functions -- Rearrangement inequalities. Brascamp-Lieb-Luttinger inequalities ; Rearrangement inequalities -- Majorization. The relative entropy.

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.

ISBN: 9780511910135Subjects--Topical Terms:

646534
Convex domains.

LC Class. No.: QA639.5 / .S56 2011

Dewey Class. No.: 516.08

Convexity = an analytic viewpoint /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Convex functions and sets -- Orlicz spaces -- Gauges and locally convex spaces -- Separation theorems -- Duality : dual topologies, bipolar sets, and Legendre transforms -- Monotone and convex matrix functions -- Loewner's theorem : a first proof -- Extreme points and the Krein-Milman theorem -- The strong Krein-Milman theorem -- Choquet theory : existence -- Choquet theory : uniqueness -- Complex interpolation -- The Brunn-Minkowski inequalities and log concave functions -- Rearrangement inequalities. Brascamp-Lieb-Luttinger inequalities ; Rearrangement inequalities -- Majorization. The relative entropy.
520 $a 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.
650 0 $a Convex domains. $3 646534
650 0 $a Mathematical analysis. $3 516833
830 0 $a Cambridge tracts in mathematics ; $v 187. $3 3470397
856 4 0 $u https://doi.org/10.1017/CBO9780511910135