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Rational Moment Problems for Compact Sets

✍ Scribed by J.D. Chandler

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 466 KB
Volume: 79
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1994.1114

No coin nor oath required. For personal study only.

✦ Synopsis

The following "rational" moment problem is discussed. Given distinct real numbers (\lambda_{1}, \lambda_{2}, \ldots, \lambda_{p}) (the "poles" of the problem), real numbers (c_{0}) and (c_{j}^{(i)}) ((j=1,2,3, \ldots ; i=1,2, \ldots, p)), and a non-empty compact subset (K) of ((-\infty,+\infty)), find necessary and sufficient conditions that there exist a non-negative Borel measure (\mu), supported on (K), such that (c_{0}=\int_{K} d \mu(t)) and (c_{j}^{(i)}=\int_{K}\left(t-\lambda_{i}\right)^{-i} d \mu(t)) for (j=1,2,3, \ldots) and (i=1,2, \ldots, p). 1994 Academic Press. Inc.

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