{
  "id": "1607.08640",
  "version": "v1",
  "published": "2016-07-28T21:08:44.000Z",
  "updated": "2016-07-28T21:08:44.000Z",
  "title": "A note on completeness of weighted Banach spaces of analytic functions",
  "authors": [
    "José Bonet",
    "Dragan Vukotić"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "Given a non-negative weight $v$, not necessarily bounded or strictly positive, defined on a domain $G$ in the complex plane, we consider the weighted space $H_v^\\infty(G)$ of all holomorphic functions on $G$ such that the product $v|f|$ is bounded in $G$ and study the question of when is such a space complete. We obtain both some necessary and some sufficient conditions, exhibit several relevant examples, and characterize completeness in the case of spaces with radial weights on balanced domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-28T21:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E15"
    ],
    "keywords": [
      "weighted banach spaces",
      "analytic functions",
      "completeness",
      "relevant examples",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}