{
  "id": "math/0504179",
  "version": "v1",
  "published": "2005-04-08T22:00:37.000Z",
  "updated": "2005-04-08T22:00:37.000Z",
  "title": "Composition Operators on the Dirichlet Space and Related Problems",
  "authors": [
    "Gerardo A. Chacon",
    "Gerardo R. Chacon",
    "Jose Gimenez"
  ],
  "comment": "8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/grchacon",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "In this paper we investigate the following problem: when a bounded analytic function $\\phi$ on the unit disk $\\mathbb{D}$, fixing 0, is such that $\\{\\phi^n : n = 0, 1, 2, . . . \\}$ is orthogonal in $\\mathbb{D}$?, and consider the problem of characterizing the univalent, full self-maps of $\\mathbb{D}$ in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of $H^2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-08T22:00:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47B33",
      "47B38",
      "47A16"
    ],
    "keywords": [
      "dirichlet space",
      "related problems",
      "hardy space",
      "bounded analytic function",
      "first problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4179C"
    }
  }
}