A set of q-coherent states for the Rogers-Szego oscillator

We discuss a model of a q-harmonic oscillator based on Rogers-Szego functions. We combine these functions with a class of q-analogs of complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new q-deformation of the m-true-polyanalytic Bargmann transform whose range defines a generalization of the Arik-Coon space. We also give an explicit formula for the reproducing kernel of this space. The obtained results may be exploited to define a q-deformation of the Ginibre-m-type process on the complex plane.