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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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
PII: S 0002-9939(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