{
  "id": "2210.15260",
  "version": "v1",
  "published": "2022-10-27T08:30:33.000Z",
  "updated": "2022-10-27T08:30:33.000Z",
  "title": "An algebraic treatment of the Pastro polynomials on the real line",
  "authors": [
    "Vutha Vichhea Chea",
    "Luc Vinet",
    "Meri Zaimi",
    "Alexei Zhedanov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The properties of the Pastro polynomials on the real line are studied with the help of a triplet of $q$-difference operators. The $q$-difference equation and recurrence relation these polynomials obey are shown to arise as generalized eigenvalue problems involving the triplet of operators, with the Pastro polynomials as solutions. Moreover, a discrete biorthogonality relation on the real line for the Pastro polynomials is obtained and is then understood using adjoint operators. The algebra realized by the triplet of $q$-difference operators is investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-27T08:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33D45",
      "47B36"
    ],
    "keywords": [
      "pastro polynomials",
      "real line",
      "algebraic treatment",
      "difference operators",
      "discrete biorthogonality relation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}