{
  "id": "2109.12095",
  "version": "v1",
  "published": "2021-09-24T17:40:35.000Z",
  "updated": "2021-09-24T17:40:35.000Z",
  "title": "Convexity of the Berezin Range",
  "authors": [
    "Carl C. Cowen",
    "Christopher Felder"
  ],
  "journal": "Linear Algebra and its Applications Volume 647, 15 August 2022, Pages 47-63",
  "doi": "10.1016/j.laa.2022.04.003",
  "categories": [
    "math.FA",
    "math.CV"
  ],
  "abstract": "This paper discusses the convexity of the range of the Berezin transform. For a bounded operator $T$ acting on a reproducing kernel Hilbert space $H$ (on a set $X$), this is the set $B(T) : = \\{ < Tk_x, k_x >_H : x \\in X \\}$, where $k_x$ is the normalized reproducing kernel for $H$ at $x \\in X$. Primarily, we focus on characterizing convexity of this range for a class of composition operators acting on the Hardy space of the unit disk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-24T17:40:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "berezin range",
      "reproducing kernel hilbert space",
      "berezin transform",
      "unit disk",
      "hardy space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}