A Reproducing Kernel Condition for Indeterminacy in the Multidimensional Moment Problem

2006/04/21 by Roger A. Roybal, Roybal, Roger A.
Mathematics · #46E22 #47A57 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E22 #msc:47A57

paper · pdf · doi:10.48550/arxiv.math/0604459

Revision: Corrected typos, updated proof of main result, added reference To appear in Proc. Amer. Math. Soc

arxiv created 2007/02/02 · arxiv updated 2009/12/01

Abstract

Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen,and Ismail's 2002 result. We also present a class of measures for which the existence of a reproducing kernel implies indeterminacy.

Related

• Small eigenvalues of large Hankel matrices:The indeterminate case
• Bounding the support of a measure from its marginal moments
• Moment indeterminateness: the Marcel Riesz variational principle
• A Note on The Multidimensional Moment Problem
• On the Berg--Chen--Ismail theorem and the Nevanlinna-Pick problem