Convexity
an analytic viewpoint
Bände/Inhalt:
- 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