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Article Dans Une Revue Infinite Dimensional Analysis, Quantum Probability and Related Topics Année : 2008

On a convolution for $q$-normal elements

Éric Ricard
Anna Kula
  • Fonction : Auteur

Résumé

In 2000 Carnovale and Koornwinder defined a $q$-convolution and proved that for some classes of measures it is associative and commutative. We investigate its positivity preserving properties. One of them is the notion of $q$-positivity related to $q$-moments. In this paper we describe an algebraic interpretation of $q$-positivity which leads us to the definition of $(p,q)$-convolution. It has a form similar to the $q$-convolution of Carnovale and Koornwinder coming from a braided algebra. For the new convolution we find an appropriate analogue of Fourier transform and also present a central limit theorem.
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Dates et versions

hal-00475256 , version 1 (21-04-2010)

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Éric Ricard, Anna Kula. On a convolution for $q$-normal elements. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2008, 11 (4), pp.565--588. ⟨10.1142/S0219025708003282⟩. ⟨hal-00475256⟩
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