Convexity :: an analytic viewpoint /
"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, Ma...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York :
Cambridge University Press,
2012, ©2011.
|
| Schriftenreihe: | Cambridge tracts in mathematics ;
187. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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 Hölder's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hölder, 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"-- |
| Beschreibung: | 1 online resource : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139637909 1139637908 9781139078771 1139078771 9780511910135 0511910134 9781139081047 1139081047 |
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| 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 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 Hölder's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hölder, 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"-- |c Provided by publisher. | ||
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| 650 | 6 | |a Algèbres convexes. | |
| 650 | 6 | |a Analyse mathématique. | |
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| author | Simon, Barry, 1946- |
| author_GND | http://id.loc.gov/authorities/names/n79082366 |
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| collection | ZDB-4-EBA |
| 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. |
| ctrlnum | (OCoLC)857791759 |
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| dewey-ones | 516 - Geometry |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| spelling | Simon, Barry, 1946- https://id.oclc.org/worldcat/entity/E39PBJbMcCjJtptX9HCWtTTmBP http://id.loc.gov/authorities/names/n79082366 Convexity : an analytic viewpoint / Barry Simon. Cambridge, UK ; New York : Cambridge University Press, 2012, ©2011. 1 online resource : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Cambridge tracts in mathematics ; 187 Print version record. Includes bibliographical references and index. 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 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 Hölder's and Minkowski's inequalities, are related to convexity. An introductory chapter (1) includes a study of regularity properties of convex functions, some inequalities (Hölder, 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"-- Provided by publisher. Convex domains. http://id.loc.gov/authorities/subjects/sh85031727 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Algèbres convexes. Analyse mathématique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Geometry General. bisacsh Convex domains fast Mathematical analysis fast has work: Convexity (Text) https://id.oclc.org/worldcat/entity/E39PCFHG7KcTfkfyp9Kj7dHYMX https://id.oclc.org/worldcat/ontology/hasWork Print version: Simon, Barry, 1946- Convexity. Cambridge, UK ; New York : Cambridge University Press, 2011 9781107007314 (DLC) 2011008617 (OCoLC)703205175 Cambridge tracts in mathematics ; 187. http://id.loc.gov/authorities/names/n42005726 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366124 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366124 Volltext |
| spellingShingle | Simon, Barry, 1946- Convexity : an analytic viewpoint / Cambridge tracts in mathematics ; 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. Convex domains. http://id.loc.gov/authorities/subjects/sh85031727 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Algèbres convexes. Analyse mathématique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Geometry General. bisacsh Convex domains fast Mathematical analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85031727 http://id.loc.gov/authorities/subjects/sh85082116 |
| title | Convexity : an analytic viewpoint / |
| title_auth | Convexity : an analytic viewpoint / |
| title_exact_search | Convexity : an analytic viewpoint / |
| title_full | Convexity : an analytic viewpoint / Barry Simon. |
| title_fullStr | Convexity : an analytic viewpoint / Barry Simon. |
| title_full_unstemmed | Convexity : an analytic viewpoint / Barry Simon. |
| title_short | Convexity : |
| title_sort | convexity an analytic viewpoint |
| title_sub | an analytic viewpoint / |
| topic | Convex domains. http://id.loc.gov/authorities/subjects/sh85031727 Mathematical analysis. http://id.loc.gov/authorities/subjects/sh85082116 Algèbres convexes. Analyse mathématique. MATHEMATICS Mathematical Analysis. bisacsh MATHEMATICS Geometry General. bisacsh Convex domains fast Mathematical analysis fast |
| topic_facet | Convex domains. Mathematical analysis. Algèbres convexes. Analyse mathématique. MATHEMATICS Mathematical Analysis. MATHEMATICS Geometry General. Convex domains Mathematical analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=366124 |
| work_keys_str_mv | AT simonbarry convexityananalyticviewpoint |