{
  "id": "1907.11670",
  "version": "v1",
  "published": "2019-07-26T16:47:19.000Z",
  "updated": "2019-07-26T16:47:19.000Z",
  "title": "Global hypoellipticity for a class of periodic Cauchy operators",
  "authors": [
    "Fernando de Ávila Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This note presents an investigation on the global hypoellipticity problem for Cauchy operators on $\\mathbb{T}^{n+1}$ belonging to the class \\linebreak $L = \\prod_{j=1}^{m}\\left(D_t + c_j(t) P_j(D_x)\\right)$, where $P_j(D_x)$ is a pseudo-differential operator on $\\mathbb{T}^n$ and $c_j = c_j(t)$, a smooth, complex valued function on $\\mathbb{T}$. The main goal of this investigation consists in establishing connections between the global hypoellipticity of the operators $L$ and its normal form $L_0 = \\prod_{j=1}^m \\left( D_t + c_{0,j}P_j(D_x)\\right)$. In order to do so, the problem is approached by combining H\\\"{o}rmander's and Siegel's conditions on the symbols of the operators $L_j = D_t + c_j(t) P_j(D_x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-26T16:47:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B10",
      "35B65",
      "35H10",
      "35S05"
    ],
    "keywords": [
      "periodic cauchy operators",
      "global hypoellipticity problem",
      "pseudo-differential operator",
      "siegels conditions",
      "complex valued function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}