The Resource Convexity : an analytic viewpoint, Barry Simon
Convexity : an analytic viewpoint, Barry Simon
Resource Information
The item Convexity : an analytic viewpoint, Barry Simon represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Convexity : an analytic viewpoint, Barry Simon represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- 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"--
- Language
- eng
- Extent
- ix, 345 pages
- 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
- Isbn
- 9781107007314
- Label
- Convexity : an analytic viewpoint
- Title
- Convexity
- Title remainder
- an analytic viewpoint
- Statement of responsibility
- Barry Simon
- 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"--
- 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
- 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Convexity--an-analytic-viewpoint-Barry/hU8kSbVr5-E/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Convexity--an-analytic-viewpoint-Barry/hU8kSbVr5-E/">Convexity : an analytic viewpoint, Barry Simon</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>
