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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...
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Printed Book |
| Γλώσσα: | English |
| Έκδοση: |
Cambridge, UK ; New York :
Cambridge University Press,
2011.
|
| Σειρά: | Cambridge tracts in mathematics ;
187. |
| Θέματα: |
Πίνακας περιεχομένων:
- 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.