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Generalization of the Hausdorff Moment Problem

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Amnon Jakimovski
David Borwein
Affiliation:
The University of Western Ontario, London, Ontario
Amnon Jakimovski
Affiliation:
Tel-Aviv University, Tel-Avivy Israel
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Suppose throughout that {kn } is a sequence of positive integers, that

that k 0 = 1 if l 0 = 1, and that {un (r)}; (r = 0, 1, …, kn – 1, n = 0, 1, …) is a sequence of real numbers. We shall be concerned with the problem of establishing necessary and sufficient conditions for there to be a function a satisfying

(1)

and certain additional conditions. The case l 0 = 0, kn = 1 for n = 0, 1, … of the problem is the version of the classical moment problem considered originally by Hausdorff [5], [6], [7]; the above formulation will emerge as a natural generalization thereof.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 4 , 01 August 1981 , pp. 946 - 960
Copyright
Copyright © Canadian Mathematical Society 1981

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