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A moment sequence in the \(q\)-world. (English) Zbl 1136.44002

Bozejko, Marek (ed.) et al., Noncommutative harmonic analysis with applications to probability. Papers presented at the 9th workshop, Bȩdlewo, Poland, September 29–October 10, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 78, 201-210 (2008).
Summary: 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 P. H. Maserick and F. H. Szafraniec [Pac. J. Math. 110, 315–324 (1984; Zbl 0489.46043)], 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.
For the entire collection see [Zbl 1128.46002].

MSC:

44A60 Moment problems
05A30 \(q\)-calculus and related topics
43A35 Positive definite functions on groups, semigroups, etc.
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)

Citations:

Zbl 0489.46043
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