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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...
| Glavni avtor: | |
|---|---|
| Format: | Printed Book |
| Jezik: | English |
| Izdano: |
Cambridge, UK ; New York :
Cambridge University Press,
2011.
|
| Serija: | Cambridge tracts in mathematics ;
187. |
| Teme: |
| LEADER | 02682cam a22003254a 4500 | ||
|---|---|---|---|
| 008 | 110303s2011 enka b 001 0 eng | ||
| 999 | |c 335135 |d 335135 | ||
| 010 | |a 2011008617 | ||
| 020 | |a 9781107007314 (hardback) | ||
| 020 | |a 1107007313 (hardback) | ||
| 035 | |a (OCoLC)ocn703205175 | ||
| 042 | |a pcc | ||
| 082 | 0 | 0 | |a 516/.08 |2 22 |
| 084 | |a MAT034000 |2 bisacsh | ||
| 100 | 1 | |a Simon, Barry, | |
| 245 | 1 | 0 | |a Convexity : |b an analytic viewpoint / |c Barry Simon. |
| 260 | |a Cambridge, UK ; |a New York : |b Cambridge University Press, |c 2011. | ||
| 300 | |a ix, 345 p. : |b ill. ; |c 24 cm. | ||
| 490 | 1 | |a Cambridge tracts in mathematics ; |v 187 | |
| 504 | |a Includes bibliographical references (p. [321]-338) and index. | ||
| 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 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"-- | ||
| 650 | 0 | |a Convex domains. | |
| 650 | 0 | |a Mathematical analysis. | |
| 942 | |c BK | ||
| 830 | 0 | |a Cambridge tracts in mathematics ; |v 187. | |
| 906 | |a 7 |b cbc |c orignew |d 1 |e ecip |f 20 |g y-gencatlg | ||
| 955 | |b re04 2011-03-03 |c re04 2011-03-03 ONIX to Gen. Science |a xe05 2011-08-05 1 copy rec'd., to CIP ver. | ||
| 955 | |a rg05 2011-8-24 Copy 3 discarded | ||
| 952 | |0 0 |1 0 |2 ddc |4 0 |6 516_000000000000000__08 |7 0 |9 383426 |a MAT |b MAT |c ST1 |d 2019-05-10 |i 5985 |l 0 |o 516/.08 |p MAT5985 |r 2019-05-10 |w 2019-05-10 |y BK | ||