Inner product spaces and minimal values of functionals

被引：0

作者：

Chelidze, G ^{[1
]}

机构：

[1] Georgian Acad Sci, N Muskhelishvili Inst Computat Math, GE-380093 Tbilisi, Georgia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 298卷 / 01期

关键词：

inner product space; Hilbert space; optimal location;

D O I：

10.1016/j.jmaa.2004.03.072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a real function which depends on the distances between a variable point and the points of a finite subset A of a linear normed space X. We show that X is an inner product space if this function attains its local minimum on a barycenter of points of A with well-chosen weights. Our result generalizes classical results about characterization of inner product spaces and answers a question of R. Durier, which was posed in his article [J. Math. Anal. Appl. 207 (1997) 220-239]. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：106 / 113

页数：8