Convexity an analytic viewpoint
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces...
| Otros Autores: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press
2011.
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| Colección: | CUP ebooks.
Cambridge tracts in mathematics ; 187. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b45438675*spi |
Tabla de Contenidos:
- 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.
