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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Simon, Barry, 1946-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge University Press, 2012, ©2011.
Colección:Cambridge tracts in mathematics ; 187.
Temas:
Convex domains.
Mathematical analysis.
Algèbres convexes.
Analyse mathématique.
MATHEMATICS > Mathematical Analysis.
MATHEMATICS > Geometry > General.
Convex domains
Mathematical analysis
Acceso en línea:Texto completo
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.

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