# Convexity : an analytic viewpoint / Barry Simon.

Material type: TextSeries: Cambridge tracts in mathematics ; 187.Publication details: Camrbridge, UK ; New York : Cambridge University Press, 2011.Description: ix, 345 p. : ill. ; 24 cmISBN:- 9781107007314 (hardback)
- 1107007313 (hardback)

- 516/.08 22

- QA639.5 .S56 2011

- MAT034000

Item type | Current library | Collection | Call number | Status | Date due | Barcode | |
---|---|---|---|---|---|---|---|

Books | School of Theoretical Physics Library | Books | 515.12 SIM (Browse shelf(Opens below)) | Available | 10973 |

Includes bibliographical references (p. [321]-338) 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 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"--

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