Every closed convex set is the set of minimizers of some C∞-smooth convex function

被引：11
|
作者：
Azagra, D [1 ]
Ferrera, J [1 ]
机构：
[1] Univ Complutense, Dept Anal Matem, Fac Ciencias Matem, E-28040 Madrid, Spain
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 130卷 / 12期
关键词：
D O I：
10.1090/S0002-9939-02-06695-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that for every closed convex set C in a separable Banach space X there is a C-infinity-smooth convex function f : X--> [0, infinity) so that f(-1) (0) = C. We also deduce some interesting consequences concerning smooth approximation of closed convex sets and continuous convex functions.
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页码：3687 / 3692
页数：6
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