{
  "id": "math/0211308",
  "version": "v3",
  "published": "2002-11-20T02:42:23.000Z",
  "updated": "2002-12-07T22:21:27.000Z",
  "title": "Non-Linear Eigenvalues and Analytic Hypoellipticity",
  "authors": [
    "Sagun Chanillo",
    "Bernard Helffer",
    "Ari Laptev"
  ],
  "comment": "22 pages, theorem 4.3 in new version is improved from m>18(old) to m>5(new) Proofs simplified considerably and typos fixed",
  "journal": "J. Functional Analysis, 209(2), 2004, 425-443",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "abstract": "Motivated by the problems of analytic hypoellipticity, we show that a special family of compact non self-adjoint operators has a non-zero eigenvalue. We recover old results by Christ,Hanges, Himonas, Pham-The-Lai and Robert proved by using ordinary differential equations. We show our method applies to higher dimensional cases, giving in particular a new class of hypoelliptic but not analytic hypoelliptic operators.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-12-07T22:21:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "35J10"
    ],
    "keywords": [
      "analytic hypoellipticity",
      "non-linear eigenvalues",
      "compact non self-adjoint operators",
      "higher dimensional cases",
      "analytic hypoelliptic operators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11308C"
    }
  }
}