A reproducing kernel condition for indeterminacy in the multidimensional moment problem

Author:
Roger A. Roybal

Journal:
Proc. Amer. Math. Soc. **135** (2007), 3967-3975

MSC (2000):
Primary 47A57; Secondary 46E22

Published electronically:
August 1, 2007

MathSciNet review:
2341947

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Roger A. Roybal**

Affiliation:
Department of Mathematics, California State University, Channel Islands, One University Drive, Camarillo, California 93012

Email:
roger.roybal@csuci.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-09007-7

Keywords:
Multidimensional moment problem,
reproducing kernel,
Hankel matrix

Received by editor(s):
May 30, 2006

Received by editor(s) in revised form:
November 11, 2006

Published electronically:
August 1, 2007

Additional Notes:
The author would like to thank Mihai Putinar for all his advice and support during the preparation of this article.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2007
American Mathematical Society