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

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 previous results obtained by the authors.