{
  "id": "2102.10714",
  "version": "v1",
  "published": "2021-02-21T23:53:17.000Z",
  "updated": "2021-02-21T23:53:17.000Z",
  "title": "A set of $q$-coherent states for the Rogers-Szegö oscillator",
  "authors": [
    "Othmane El Moize",
    "Zouhaïr Mouayn"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss a model of a $q$-harmonic oscillator based on Rogers-Szeg\\\"o 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-21T23:53:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coherent states",
      "complex hermite polynomials",
      "true-polyanalytic bargmann transform",
      "harmonic oscillator",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}