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The Resource Convexity : an analytic viewpoint, Barry Simon

Convexity : an analytic viewpoint, Barry Simon

Label
Convexity : an analytic viewpoint
Title
Convexity
Title remainder
an analytic viewpoint
Statement of responsibility
Barry Simon
Creator
Subject
Language
eng
Summary
"Convexity of sets and functions are extremely simple notions to define, so it may be somewhat surprising the depth and breadth of ideas that these notions give rise to. It turns out that convexity is central to a vast number of applied areas, including Statistical Mechanics, Thermodynamics, Mathematical Economics, and Statistics, and that many inequalities, including Hl̲der's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hl̲der, Minkowski, and Jensen), the Hahn-Banach theorem as a statement about extending tangents to convex functions, and the introduction of two constructions that will play major roles later in this book: the Minkowski gauge of a convex set and the Legendre transform of a function"--
Member of
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorDate
1946-
http://library.link/vocab/creatorName
Simon, Barry
Dewey number
516/.08
Illustrations
illustrations
Index
index present
LC call number
QA639.5
LC item number
.S56 2011
Literary form
non fiction
Nature of contents
bibliography
Series statement
Cambridge tracts in mathematics
Series volume
187
http://library.link/vocab/subjectName
  • Convex domains
  • Mathematical analysis
  • MATHEMATICS / Mathematical Analysis
Label
Convexity : an analytic viewpoint, Barry Simon
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
703205175
Dimensions
24 cm
Extent
ix, 345 pages
Isbn
9781107007314
Lccn
2011008617
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)703205175
Label
Convexity : an analytic viewpoint, Barry Simon
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
703205175
Dimensions
24 cm
Extent
ix, 345 pages
Isbn
9781107007314
Lccn
2011008617
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
System control number
(OCoLC)703205175

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