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Uniqueness criterion for a moment problem

Published online by Cambridge University Press:  09 April 2009

A. Lenard
A. Lenard
Affiliation:
Institute of Advanced Study, Princeton, New Jersey 08540, U.S.A.
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In an article that appeared some years ago in this journal, Takács [1] gave a uniqueness criterion for the solution of the moment problem where the Br are given numbers and the Pk are sought, Pk ≧ 0, σkPk = 1. Takács showed that if Br < ∞ for all r and then the solution is unique. In addition, he gave an explicit formula for the solution in this case where q is any number satisfying q ≧ 0 and q > p2 — 1.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 303 - 305
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Takács, L., ‘A moment problem’, J. Austral. Math. Soc. 5 (1965), 487–490.CrossRefGoogle Scholar
[2]Carleman, T., Les Fonctions Quasi-Analytiques (Gauthier-Villars, Paris, 1926) Chapter III.Google Scholar