A Reproducing Kernel Condition for Indeterminacy in the Multidimensional Moment Problem

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.

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