{
  "id": "math/0609777",
  "version": "v1",
  "published": "2006-09-28T01:25:30.000Z",
  "updated": "2006-09-28T01:25:30.000Z",
  "title": "Analytic Hypoellipticity at Non-Symplectic Poisson-Treves Strata for Sums of Squares of Vector Fields",
  "authors": [
    "Antonio Bove",
    "David S. Tartakoff"
  ],
  "comment": "20pp",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \\sigma $ is not constant on $ \\Char P $. Moreover the Hamilton foliation of the non symplectic stratum of the Poisson-Treves stratification for $ P $ consists of closed curves in a ring-shaped open set around the origin. We prove that then $ P $ is analytic hypoelliptic on that open set. And we note explicitly that the local Gevrey hypoellipticity for $ P $ is $ G^{k+1} $ and that this is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-28T01:25:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "35N15"
    ],
    "keywords": [
      "non-symplectic poisson-treves strata",
      "vector fields",
      "analytic hypoellipticity",
      "open set",
      "local gevrey hypoellipticity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9777B"
    }
  }
}