{
  "id": "math-ph/0405010",
  "version": "v4",
  "published": "2004-05-04T14:47:36.000Z",
  "updated": "2006-07-23T11:14:23.000Z",
  "title": "Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators",
  "authors": [
    "Felix Finster",
    "Harald Schmid"
  ],
  "comment": "33 pages, LaTeX, 3 figures, typo in Lemma 4.1 corrected (published version)",
  "journal": "J. Reine Angew. Math. 601 (2006) 71-107",
  "doi": "10.1515/CRELLE.2006.095",
  "categories": [
    "math-ph",
    "gr-qc",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $\\Omega$ in a neighborhood of the real line. For real $\\Omega$, estimates are derived for all eigenvalue gaps uniformly in $\\Omega$. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $\\Omega$ is derived using the theory of slightly non-selfadjoint perturbations.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2006-07-23T11:14:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral estimates",
      "spectral representation",
      "oblate spheroidal wave operator",
      "slightly non-selfadjoint perturbations",
      "complex solutions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 649710,
      "adsabs": "2004math.ph...5010F"
    }
  }
}