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A reproducing kernel condition for indeterminacy in the multidimensional moment problem
Author(s):
Roger
A.
Roybal
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3967-3975.
MSC (2000):
Primary 47A57;
Secondary 46E22
Posted:
August 1, 2007
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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.
References:
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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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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