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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Hamburger moment problems and orthogonal polynomials


Author: T. S. Chihara
Journal: Trans. Amer. Math. Soc. 315 (1989), 189-203
MSC: Primary 42C05; Secondary 30E05, 33A65, 44A60
MathSciNet review: 986686
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Abstract: We consider a sequence of orthogonal polynomials given by the classical three term recurrence relation. We address the problem of deciding the determinacy or indeterminacy of the associated Hamburger moment problem on the basis of the behavior of the coefficients in the three term recurrence relation. Comparisons are made with other criteria in the literature. The efficacy of the criteria obtained is illustrated by application to many specific examples of orthogonal polynomials.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0986686-1
PII: S 0002-9947(1989)0986686-1
Keywords: Moment problems, orthogonal polynomials, recurrence relations, chain sequences
Article copyright: © Copyright 1989 American Mathematical Society