Smallest and largest generalized eigenvalues of large moment matrices and some applications

被引：1

作者：

Escribano, C. ^{[1
]}

Gonzalo, R. ^{[2
]}

Torrano, E. ^{[2
]}

机构：

[1] Univ Politecn Madrid, Escuela Tecn Super Ingn Informat & Ctr Computat Si, Dept Matemat Aplicada Tecnol Informac & Comunicac, Campus Montegancedo Boadilla Monte, Madrid 28660, Spain

[2] Univ Politecn Madrid, Escuela Tecn Super Ingn Informat, Dept Matemat Aplicada Tecnol Informac & Comunicac, Campus Montegancedo Boadilla Monte, Madrid 28660, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 521卷 / 02期

关键词：

Hermitian moment problem; Orthogonal polynomials; Smallest eigenvalue; Measures; Approximation by polynomials; LARGE HANKEL-MATRICES;

D O I：

10.1016/j.jmaa.2022.126959

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main aim of this work is to compare two Borel measures thorough their moment matrices using a new notion of smallest and largest generalized eigenvalues. With this approach we provide information in problems as the localization of the support of a measure. In particular, we prove that if a measure is comparable in an algebraic way with a measure in a Jordan curve then the curve is contained in its support. We obtain a description of the convex envelope of the support of a measure via certain Rayleigh quotients of certain infinite matrices. Finally some applications concerning polynomial approximation in mean square are given, generalizing previous results obtained by the authors.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：16

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