Extremal measures with prescribed moments

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:423

Article

Rajba, Teresa¹  Wasowicz, Szymon¹ 

[1] Univ Bielsko Biala, Dept Math & Comp Sci, PL-43309 Bielsko Biala, Poland

关键词: Choquet Representation Theorem;    Convex functions of higher order;    Extreme point of a convex set;    Extremalities in the approximate integration;    Probability measure;    Quadrature;   

DOI  :  10.1016/j.jmaa.2014.11.001

来源: Elsevier

【 摘 要 】

In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called extrernalities. On the other hand, the set of all quadratures is convex. We are trying to find possible connections between extrernalities and extremal quadratures (in the sense of extreme points of a convex set). Of course, the quadratures are the integrals with respect to discrete measures and, moreover, a quadrature is extremal if and only if the associated measure is extremal. Hence the natural problem arises to give some description of extremal measures with prescribed moments in the general (not only discrete) case. In this paper we deal with symmetric measures with prescribed first four moments. The full description (with no symmetry assumptions, and/or not only four moments are prescribed and so on) is far to be done. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free