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arXiv · 2006.14083

A q deformation of true-polyanalytic Bargmann transforms when q^{-1}> 1

Othmane El moize·Zouhair Mouayn
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Abstract

We combine continuous $q^{-1}$-Hermite Askey polynomials with new $2D$ orthogonal polynomials introduced by Ismail and Zhang as $q$-analogs for complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter $m$. In the analytic case corresponding to $m=0$, we recover a known result on the Ar\"{\i}k-Coon oscillator for $q'=q^{-1}>1$. Our construction leads to a new $q$-deformation of the $m$-true-polyanalytic Bargmann transform on the complex plane. The obtained result may be used to introduce a $q$-deformed Ginibre-type point process.

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Othmane El moize, Zouhair Mouayn. 2020-06-24. A q deformation of true-polyanalytic Bargmann transforms when q^{-1}> 1. https://arxiv.org/abs/2006.14083

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