{
  "id": "math/0603317",
  "version": "v2",
  "published": "2006-03-14T02:20:33.000Z",
  "updated": "2006-09-28T09:53:49.000Z",
  "title": "Analytic Hypoellipticity in the Presence of Lower Order Terms",
  "authors": [
    "Paolo Albano",
    "Antonio Bove",
    "David S. Tartakoff"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of the characteristic manifold. In the $C^\\infty$ framework this situation would mean a loss of 3/2 derivatives. We prove that this operator is analytic hypoelliptic. The main tool is the FBI transform. A case in which $C^\\infty$ hypoellipticity fails is also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-09-28T09:53:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H10",
      "35N15"
    ],
    "keywords": [
      "lower order terms",
      "analytic hypoellipticity",
      "symplectic real analytic manifold",
      "second order operator",
      "analytic coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3317A"
    }
  }
}