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A moment sequence in the $q$-world

Tom 78 / 2007

Anna Kula Banach Center Publications 78 (2007), 201-210 MSC: Primary 44A60; Secondary 05A30, 43A35, 47B32. DOI: 10.4064/bc78-0-15

Streszczenie

The aim of the paper is to present some initial results about a possible generalization of moment sequences to a so-called $q$-calculus. A characterization of such a $q$-analogue in terms of appropriate positivity conditions is also investigated. Using the result due to Maserick and Szafraniec, we adapt a classical description of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity to the $q$-situation. This makes a link between $q$-positive definiteness and $q$-complete monotonicity.

Autorzy

  • Anna KulaInstitute of Mathematics
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland
    e-mail

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