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On certain non-unique solutions of the Stieltjes moment problem

By Karol A. Penson, Pawel Blasiak, Gerard H. E. Duchamp, Andrzej Horzela and Allan I. Solomon

Abstract

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]<sup>2</sup>. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Year: 2010
OAI identifier: oai:oro.open.ac.uk:22209
Provided by: Open Research Online

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