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

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. Our construction leads to a new qdeformation of the m-true-polyanalytic Bargmann transform on the complex plane. In the analytic case m = 0, the obtained coherent states transform can be associated with the Arïk-Coon oscillator for q = q −1 > 1. These result may be used to introduce a q-deformed Ginibre-type point process.