An Analytic Viewpoint
by Barry Simon (Caltech)


To order from Cambridge University Press

Table of Contents

1. Convex functions and sets
2. Orlicz spaces
3. Gauges and locally convex spaces
4. Separation theorems
5. Duality: dual topologies, bipolar sets, and Legendre transforms
6. Monotone and convex matrix functions
7. Loewner's theorem: a first proof
8. Extreme points and the Krein–Milman theorem
9. The strong Krein–Milman theorem
10. Choquet theory: existence
11. Choquet theory: uniqueness
12. Complex interpolation
13. The Brunn–Minkowski inequalities and log concave functions
14. Rearrangement inequalities: a) Brascamp–Lieb–Luttinger inequalities
15. Rearrangement inequalities: b) Majorization
16. The relative entropy
17. Notes
Author index
Subject index

Sample Chapter


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