{
  "id": "2207.09015",
  "version": "v1",
  "published": "2022-07-19T01:41:32.000Z",
  "updated": "2022-07-19T01:41:32.000Z",
  "title": "Composition-differentiation operators on the Dirichlet space",
  "authors": [
    "Robert F. Allen",
    "Katherine Heller",
    "Matthew A. Pons"
  ],
  "journal": "J. Math. Anal. Appl. 512 (2022), no. 2, Paper No. 126186, 18 pp",
  "doi": "10.1016/j.jmaa.2022.126186",
  "categories": [
    "math.FA"
  ],
  "abstract": "We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition, for particular classes of inducing maps, we derive an adjoint formula, compute the norm, and identify the spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-19T01:41:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33"
    ],
    "keywords": [
      "dirichlet space",
      "hilbert-schmidt composition-differentiation operators",
      "adjoint formula",
      "determine characterizations",
      "unit disk"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}