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

• 成果类型: Article
• 署名作者: Artstein-Avidan, Shiri; Milman, Vitali
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.661
• 发表日期: 2009
• 页码: 661-674
• 关键词: endomorphisms; lattice

摘要

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.