Small eigenvalues of large Hankel matrices:The indeterminate case

1999/07/16 by Christian Berg, Yang Chen, Berg, Christian +3 · 1 citation
Mathematics · #31A15 #33C25 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:31A15 #msc:33C25 #msc:42C05

paper · pdf · doi:10.48550/arxiv.math/9907110

14 pages, 1 figure

arxiv created 1999/07/16 · arxiv updated 2009/11/30

Abstract

In this paper we characterise the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expresions for this lower bound in a number of indeterminate moment problems.

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• Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions

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