{
  "id": "2207.12635",
  "version": "v1",
  "published": "2022-07-26T03:44:03.000Z",
  "updated": "2022-07-26T03:44:03.000Z",
  "title": "Compact differences of composition operators on weighted Dirichlet spaces",
  "authors": [
    "Robert F. Allen",
    "Katherine Heller",
    "Matthew A. Pons"
  ],
  "journal": "Cent. Eur. J. Math. 12 (2014), no. 7, 1040-1051",
  "doi": "10.2478/s11533-013-0397-3",
  "categories": [
    "math.FA"
  ],
  "abstract": "Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\\mathcal{D}_\\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calder\\'{o}n's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-26T03:44:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "46E20",
      "47B32"
    ],
    "keywords": [
      "composition operators",
      "compact differences",
      "general weighted dirichlet spaces",
      "linear fractional self-maps",
      "analytic functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}