{
  "id": "1206.3455",
  "version": "v1",
  "published": "2012-06-15T13:14:40.000Z",
  "updated": "2012-06-15T13:14:40.000Z",
  "title": "Regularity of class of differential operators",
  "authors": [
    "Ernesto Buzano",
    "Alessandro Oliaro"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we deal with the problem of regularity for non hypo-elliptic partial differential equations with polynomial coefficients. An operator $A$ on on the space of tempered distributions $\\mathcal{S}^\\prime$ is regular if $u$ belongs to the Schwartz class $\\mathcal S$ whenever $Au\\in \\mathcal S$. By using tensor products of topological vector spaces and a kind of Wigner transform we reduce the study of regularity of a non hypo-elliptic differential operator, like the twisted laplacian, to a hypo-elliptic one, like the harmonic oscillator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-15T13:14:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35H99"
    ],
    "keywords": [
      "regularity",
      "non hypo-elliptic partial differential equations",
      "non hypo-elliptic differential operator",
      "schwartz class",
      "tensor products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.3455B"
    }
  }
}