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

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.