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The Sobolev-type moment problem

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URI: http://hdl.handle.net/10016/6143
ISSN: 0002-9939 (Print)
ISSN: 1088-6826 (Online)
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sobolev_marcellan_pams_2000.pdf (167.68 KB)
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2000-08
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American Mathematical Society
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Abstract
We propose necessary and sufficient conditions for a bisequence of complex numbers to be a moment one of Sobolev type over the real line, the unit circle and the complex plane. We achieve this through converting the moment problem in question into a matrix one and utilizing some techniques coming from operator theory. This allows us to consider the Sobolev type moment problem in its full generality, not necessarily in the diagonal case and even of infinite order.
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9 pages, no figures.-- MSC2000 codes: Primary 44A99; Secondary 47B15, 47B20, 47B25.
MR#: MR1694873 (2000k:44006)
Zbl#: Zbl 0951.44002
Keywords
Sobolev-type moment problem, Positive operators, Inner product, Orthogonal polynomials, Moment sequence of Sobolev type, Matrix moment problems
Bibliographic citation
Proceedings of the American Mathematical Society, 2000, vol. 128, n. 8, p. 2309-2317
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