{
  "id": "1501.04698",
  "version": "v1",
  "published": "2015-01-20T02:29:17.000Z",
  "updated": "2015-01-20T02:29:17.000Z",
  "title": "Spectral analysis for the exceptional $X_m$-Jacobi equation",
  "authors": [
    "Constanze Liaw",
    "Lance Littlejohn",
    "Jessica Stewart"
  ],
  "comment": "Submitted. 9 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We provide the mathematical foundation for the $X_m$-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional $X_m$-Jacobi orthogonal polynomials as eigenfunctions. This proves that those polynomials are indeed eigenfunctions of the self-adjoint operator (rather than just formal eigenfunctions). Further, we prove the completeness of the exceptional $X_m$-Jacobi orthogonal polynomials (of degrees $m, m+1, m+2, ...$) in the Lebesgue--Hilbert space with the appropriate weight. In particular, the self-adjoint operator has no other spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-20T02:29:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33C45",
      "34B24",
      "42C05",
      "33C47",
      "47B25"
    ],
    "keywords": [
      "jacobi equation",
      "spectral analysis",
      "self-adjoint operator",
      "jacobi orthogonal polynomials",
      "exceptional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104698L"
    }
  }
}