Smallest and largest generalized eigenvalues of large moment matrices and some applications
Functional Analysis
2022-03-30 v1 Spectral Theory
Abstract
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 the results in [9].
Cite
@article{arxiv.2203.15453,
title = {Smallest and largest generalized eigenvalues of large moment matrices and some applications},
author = {C. Escribano and R. Gonzalo and E. Torrano},
journal= {arXiv preprint arXiv:2203.15453},
year = {2022}
}