The concept of duality in convex analysis, and the characterization of the Legendre transform
The concept of duality in convex analysis, and the characterization of the Legendre transform
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DOI：
10.4007/annals.2009.169.661
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发表时间：
2009-03
影响因子：
4.9
通讯作者：
S. Artstein-Avidan;V. Milman
中科院分区：
文献类型：
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作者：
S. Artstein-Avidan;V. Milman
在本文的主要定理中，我们证明了下半连续凸函数类上的任意对合，只要是反序的，在线性项之前，都必须是著名的勒让德变换。
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.