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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About

• Item ORO ID
• 22209
• Item Type
• Journal Item
• ISSN
• 1365-8050
• Keywords
• Stieltjes moment problem; Mellin transform
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Physical Sciences
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2010 Discrete Mathematics and Theoretical Computer Science (DMTCS)
• Depositing User
• Allan Solomon