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Moment problems related to Bernstein functions
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 577-594.

Nous donnons une preuve simple du caractère indéterminé sur la demi-droite de la suite de moments entiers (n!) t pour t>2, à l’aide de la condition de Lin. Sous une hypothèse d’auto-décomposabilité logarithmique, la méthode s’étend à des suites de puissances de moments entiers définis comme la factorielle croissante d’une fonction de Bernstein donnée, et plus généralement à d’autres suites infiniment divisibles de moments entiers. Nous donnons aussi une preuve très courte du caractère infiniment divisible de toutes les suites de moments entiers récemment étudiées dans [16] et en particulier de la suite de Fuss–Catalan.

We give a simple proof of the moment-indeterminacy on the half-line of the sequence (n!) t for t>2, using Lin’s condition. Under a logarithmic self-decomposability assumption, the method conveys to power moment sequences defined as the rising factorials of a given Bernstein function, and to more general infinitely divisible moment sequences. We also provide a very short proof of the infinite divisibility of all the integer moment sequences recently investigated in [16], including Fuss–Catalan’s.

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DOI : https://doi.org/10.5802/afst.1640
Classification : 44A60,  60E05,  60G51
Mots clés : Bernstein function, Fuss–Catalan number, Moment problem, Moment sequence, Remainder
@article{AFST_2020_6_29_3_577_0,
     author = {Thomas Simon},
     title = {Moment problems related to Bernstein functions},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {577--594},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 29},
     number = {3},
     year = {2020},
     doi = {10.5802/afst.1640},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1640/}
}
Thomas Simon. Moment problems related to Bernstein functions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 3, pp. 577-594. doi : 10.5802/afst.1640. https://afst.centre-mersenne.org/articles/10.5802/afst.1640/

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