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A Fuss-type family of positive definite sequences

Volume 151 / 2018

Wojciech Młotkowski, Karol A. Penson Colloquium Mathematicum 151 (2018), 289-304 MSC: Primary 44A60; Secondary 33C20, 46L54. DOI: 10.4064/cm6894-2-2017 Published online: 12 January 2018


We study a two-parameter family $a_{n}(p,t)$ of deformations of the Fuss numbers. We show a sufficient condition for positive definiteness of $a_n(p,t)$ and prove that some of the corresponding probability measures are infinitely divisible with respect to the additive free convolution.


  • Wojciech MłotkowskiInstytut Matematyczny
    Uniwersytet Wrocławski
    Plac Grunwaldzki 2/4
    50-384 Wrocław, Poland
  • Karol A. PensonSorbonne Universités
    Université Pierre et Marie Curie
    Laboratoire de Physique Théorique
    de la Matière Condensée
    CNRS UMR 7600, Tour 13, 5ième ét.
    Boîte Courrier 121, 4 place Jussieu
    F-75252 Paris Cedex 05, France

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