{
  "id": "1802.01831",
  "version": "v1",
  "published": "2018-02-06T07:41:26.000Z",
  "updated": "2018-02-06T07:41:26.000Z",
  "title": "Estimate for norm of a composition operator on the Hardy-Dirichlet space",
  "authors": [
    "Perumal Muthukumar",
    "Saminathan Ponnusamy",
    "Hervé Queffélec"
  ],
  "comment": "12 pages, one figure; To appear in Integral Equations and Operator Theory",
  "categories": [
    "math.FA"
  ],
  "abstract": "By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $\\mathcal{H}^2$, the space of Dirichlet series with square summable coefficients, for the inducing symbol $\\varphi(s)=c_1+c_{q}q^{-s}$ where $q\\geq 2$ is a fixed integer. We also give an estimate on the approximation numbers of such an operator.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T07:41:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "47B38",
      "11M36",
      "37C30"
    ],
    "keywords": [
      "composition operator",
      "hardy-dirichlet space",
      "schur test",
      "lower estimates",
      "dirichlet series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}