{
  "id": "1712.00280",
  "version": "v1",
  "published": "2017-12-01T11:33:17.000Z",
  "updated": "2017-12-01T11:33:17.000Z",
  "title": "Monomial basis in Korenblum type spaces of analytic functions",
  "authors": [
    "José Bonet",
    "Wolfgang Lusky",
    "Jari Taskinen"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is shown that the monomials $\\Lambda=(z^n)_{n=0}^{\\infty}$ are a Schauder basis of the Fr\\'echet spaces $A_+^{-\\gamma}, \\ \\gamma \\geq 0,$ that consists of all the analytic functions $f$ on the unit disc such that $(1-|z|)^{\\mu}|f(z)|$ is bounded for all $\\mu > \\gamma$. Lusky \\cite{L} proved that $\\Lambda$ is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type $H^{\\infty}$. A sequence space representation of the Fr\\'echet space $A_+^{-\\gamma}$ is presented. The case of (LB)-spaces $A_{-}^{-\\gamma}, \\ \\gamma > 0,$ that are defined as unions of weighted Banach spaces is also studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-01T11:33:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E10",
      "46A35",
      "46A45",
      "46E15"
    ],
    "keywords": [
      "analytic functions",
      "korenblum type spaces",
      "monomial basis",
      "weighted banach spaces",
      "frechet space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}