Convexity : an analytic viewpoint [E-Book] / Barry Simon.
Simon, Barry, (author)
Cambridge : Cambridge University Press, 2011
1 online resource (ix, 345 pages)
englisch
9781107471368
9781107007314
9780511910135
Cambridge tracts in mathematics ; 187
Full Text
Table of Contents:
  • 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.