{
  "id": "2307.12819",
  "version": "v1",
  "published": "2023-07-24T14:14:42.000Z",
  "updated": "2023-07-24T14:14:42.000Z",
  "title": "Schwartz regularity of differential operators on the cylinder",
  "authors": [
    "André Pedroso Kowacs"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2306.15578",
  "categories": [
    "math.AP"
  ],
  "abstract": "This article presents an investigation of global properties of a class of differential operators on $\\T^1\\times\\R$. Our approach involves the utilization of a mixed Fourier transform, incorporating both partial Fourier series on the torus and partial Fourier transform in Euclidean space. By examining the behavior of the mixed Fourier coefficients, we obtain necessary and sufficient conditions for the Schwartz global hypoellipticity of this class of differential operators, as well as conditions for the Schwartz global solvability of said operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-24T14:14:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential operators",
      "schwartz regularity",
      "partial fourier transform",
      "schwartz global solvability",
      "schwartz global hypoellipticity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}