{
  "id": "2301.06353",
  "version": "v1",
  "published": "2023-01-16T10:53:17.000Z",
  "updated": "2023-01-16T10:53:17.000Z",
  "title": "Composition operators on Gelfand-Shilov classes",
  "authors": [
    "Héctor Ariza",
    "Carmen Fernández",
    "Antonio Galbis"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study composition operators on global classes of ultradifferentiable functions of Beurling type invariant under Fourier transform. In particular, for the classical Gelfand-Shilov classes $\\Sigma_d,\\ d > 1,$ we prove that a necessary condition for the composition operator $f\\mapsto f\\circ \\psi$ to be well defined is the boundedness of $\\psi'.$ We find the optimal index $d'$ for which $C_\\psi(\\Sigma_d({\\mathbb R}))\\subset \\Sigma_{d'}({\\mathbb R})$ holds for any non-constant polynomial $\\psi.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T10:53:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "46F05"
    ],
    "keywords": [
      "study composition operators",
      "optimal index",
      "global classes",
      "non-constant polynomial",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}