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

Shiri Artstein-Avidan*, Vitali Milman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)661-674
Number of pages14
JournalAnnals of Mathematics
Volume169
Issue number2
DOIs
StatePublished - 2009

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