{
  "id": "1507.08880",
  "version": "v1",
  "published": "2015-07-31T13:56:17.000Z",
  "updated": "2015-07-31T13:56:17.000Z",
  "title": "Global Hypoellipticity for First-Order Operators on Closed Smooth Manifolds",
  "authors": [
    "Fernando de Ávila Silva",
    "Alexandre Kirilov",
    "Todor Gramchev"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The main goal of this paper is to address global hypoellipticity issues for the following class of operators: $L = D_t + C(t,x,D_x)$, where $(t,x) \\in \\mathbb{T} \\times M$, $\\mathbb{T}$ is the one-dimensional torus, $M$ is a closed manifold and $C(t,x,D_x)$ is a first order pseudo-differential operator on $M$, smoothly depending on the periodic variable $t$. In the case of separation of variables, namely, $C(t,x,D_x) = a(t)p(x,D_x)+ib(t)q(x,D_x)$, we give necessary and sufficient conditions for the global hypoellipticity of $L$. In particular, we show that, under suitable conditions, the famous (P) condition of Niremberg-Treves is neither necessary nor sufficient to guarantee the global hypoellipticity of $L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-31T13:56:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35F05",
      "35S05",
      "58J40"
    ],
    "keywords": [
      "closed smooth manifolds",
      "first-order operators",
      "address global hypoellipticity issues",
      "first order pseudo-differential operator",
      "main goal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150708880D"
    }
  }
}