Kula, Anna 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) Keywords:moment problems; positive definiteness; complete monotonicity; \(q\)-calculus; reproducing kernel; Hausdorff moment sequences Citations:Zbl 0489.46043 PDFBibTeX XMLCite \textit{A. Kula}, Banach Cent. Publ. 78, 201--210 (2008; Zbl 1136.44002)