{
  "id": "math/9408209",
  "version": "v1",
  "published": "1994-08-24T00:00:00.000Z",
  "updated": "1994-08-24T00:00:00.000Z",
  "title": "The Askey-Wilson polynomials and q-Sturm-Lioville problems",
  "authors": [
    "B. Malcolm Brown",
    "William Desmond Evans",
    "Mourad E. H. Ismail"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-08-24T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "askey-wilson polynomials",
      "q-sturm-lioville problems",
      "cauchy principle value",
      "askey-wilson divided difference operator",
      "operator theoretic description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}