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

Moment problems for compact sets


Author: J. D. Chandler
Journal: Proc. Amer. Math. Soc. 104 (1988), 1134-1140
MSC: Primary 44A60; Secondary 42A70, 47B15
MathSciNet review: 942632
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Abstract: The solvability of the Hausdorff moment problem for an arbitrary compact subset of Euclidean $ n$-space is shown to be equivalent to the nonnegativity of a family of quadratic forms derived from the given moment sequence and the given compact set. A variant theorem for the one-dimensional case and an analogous theorem for the trigonometric moment problem are also given. The one-dimensional theorems are similar to theorems of Kreĭn and Nudel'man [11], but the proofs, unlike those in [11], do not depend on the existence of a standard form for polynomials which are nonnegative on a given compact set.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0942632-2
PII: S 0002-9939(1988)0942632-2
Article copyright: © Copyright 1988 American Mathematical Society