On certain non-unique solutions of the Stieltjes moment problem

Penson, Karol A.; Blasiak, Pawel; Duchamp, Gerard H. E.; Horzela, Andrzej and Solomon, Allan I. (2010). On certain non-unique solutions of the Stieltjes moment problem. Discrete Mathematics & Theoretical Computer Science, 12(2) pp. 295–306.

URL: http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/art...

Abstract

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. 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.

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