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Abstract

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.