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Unique solvability of the strong Hamburger moment problem

Part of: Miscellaneous topics of analysis in the complex domain

Published online by Cambridge University Press:  09 April 2009

Olav Njåstad  and
W. J. Thron
Olav Njåstad
Affiliation:
Department of Mathematics, University of Trondeim, N-7034 Trondheim-NTH, Norway
W. J. Thron
Affiliation:
Department of Mathematics, Campus Box 426, University of Colorado, Boulder, Colorado 80309, U.S.A.
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Abstract

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Methods from the theory of orthogonal polynomials are extended to L-polynomials . By this means the authors and W. B. Jones (J. Math. Anal. Appl. 98 (1984), 528–554) solved the strong Hamburger moment problem, that is, given a double sequence , to find a distribution function ψ(t), non-decreasing, with an infinitenumber of points of increase and bounded on −∞ < t < ∞, such that for all integers . In this article further menthods such as analogues of the Lioville-Ostrogradski formula and of the Christoffel-Darboux formula are developed to investigated When the moment porblem has a unique solution. This will be the case if and only if a sequence of nested disks associated with the sequence has only a point as its intersection (the so called limit point case).

MSC classification

Secondary: 30E05: Moment problems, interpolation problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 5 - 19
Copyright
Copyright © Australian Mathematical Society 1986

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