{
  "id": "math/0504159",
  "version": "v1",
  "published": "2005-04-07T21:43:09.000Z",
  "updated": "2005-04-07T21:43:09.000Z",
  "title": "Analytic Hypoellipticity for a Class of Sums of Squares of Vector Fields with Non-Symplectic Characteristic Variety",
  "authors": [
    "Antonio Bove",
    "Makhlouf Derridj",
    "David S. Tartakoff"
  ],
  "comment": "11 pages",
  "journal": "Journal of Functional Analysis {\\bf 234} (2), (2006), pp~464-472.",
  "categories": [
    "math.AP",
    "math.CV",
    "math.SG"
  ],
  "abstract": "The recent example of Hanges: $P = \\partial_t^2 + t^2\\Delta_x + \\partial^2_{\\theta(x)}$ in $R^3$ is analytic hypoelliptic in the sense of germs but not in the strong sense in any neighborhood of the origin. And its characteristic variety is non-symplectic. We give a purely $L^2,$ and hence quite flexible, proof of this result and generalizations, and link it to, and contrast it with, the celebrated Baouendi-Goulaouic operator. We point out that the results are consistent with the conjecture of Treves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-07T21:43:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "35N15"
    ],
    "keywords": [
      "non-symplectic characteristic variety",
      "analytic hypoellipticity",
      "vector fields",
      "strong sense",
      "celebrated baouendi-goulaouic operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4159B"
    }
  }
}