{
  "abstract": "We explore properties of the Berezin range $B(C_ϕ)$ of a composition operator $C_ϕ$ on the Hardy space $H^2$, including constraints on its location in the complex plane $\\mathbb{C}$, topological properties, shape, symmetry, and convexity. For example, we show that $B(C_ϕ) \\subseteq \\{z\\in \\mathbb{C}: \\Re(z) > 0 \\ \\text{and}\\ |z| \\le 1 + |ϕ(0)|\\}$, that $B(C_ϕ)$ is closed if and only if $C_ϕ$ is the identity operator, and that $B(C_ϕ)$ containa all its boundary points except for $0$ if $C_ϕ$ is compact. Addressing questions raised by Cowen and Felder, we show that $C_ϕ$ can be a (nondegenerate) disk and characterize when $B(C_ϕ)$ is convex if $ϕ$ is linear.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17634",
  "author_total": 3,
  "authors": [
    {
      "name": "Paul Bourdon"
    },
    {
      "name": "Trieu Le"
    },
    {
      "name": "Derek Thompson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tg4d0hna6j8s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17634",
  "fulltext_url": null,
  "id": "4tg4d0hna6j8s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17634",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7221803698",
  "pdf_url": "https://arxiv.org/pdf/2610.17634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tg4d0hna6j8s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Berezin Ranges of Composition Operators on $H^2$",
  "title_text": "Berezin Ranges of Composition Operators on H^2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4tg4d0hna6j8s",
  "venue": "arXiv",
  "versions": []
}