Discrete Mathematics & Theoretical Computer Science, Vol 12, No 2 (2010)

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On certain non-unique solutions of the Stieltjes moment problem

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


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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