The concept of duality in convex analysis, and the characterization of the Legendre transform

Abstract

In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform.

Authors

Shiri Artstein-Avidan

School of Mathematical Sciences
Tel Aviv University
Tel Aviv 69978
Israel

Vitali Milman

School of Mathematical Sciences
Tel Aviv University
Tel Aviv 69978
Israel