Table of Contents

Preface; 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; References; Author index; Subject index.

Promotional Information

A comprehensive look at convexity and its mathematical ramifications.

About the Author

Barry Simon is IBM Professor of Mathematics and Theoretical Physics at the California Institute of Technology.

Reviews

"Simon's monograph is a valuable addition to the literature on convexity that will inspire many minds enchanted by the beauty and power of the cornerstone of functional analysis."
S. Kutateladze, Mathematical Reviews