000			02866nam a22003738i 4500
001			CR9780511910135
003			UkCbUP
005			20200124160240.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100811s2011||||enk o ||1 0|eng|d
020			_a9780511910135 (ebook)
020			_z9781107007314 (hardback)
020			_z9781107471368 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA639.5 _b.S56 2011
082	0	0	_a516/.08 _222
100	1		_aSimon, Barry, _d1946- _eauthor.
245	1	0	_aConvexity : _ban analytic viewpoint / _cBarry Simon.
264		1	_aCambridge : _bCambridge University Press, _c2011.
300			_a1 online resource (ix, 345 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v187
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aConvex 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			_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		0	_aConvex domains.
650		0	_aMathematical analysis.
776	0	8	_iPrint version: _z9781107007314
830		0	_aCambridge tracts in mathematics ; _v187.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511910135
999			_c518475 _d518473