{
  "abstract": "By constructing an appropriate quadratic form, we prove that if an analytic Toeplitz operator commutes with a co-analytic Toeplitz operator on the harmonic Bergman space, then at least one of the symbols is constant. This resolves an open question posed by Choe and Lee in 1999.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14635",
  "author_total": 3,
  "authors": [
    {
      "name": "Xianchi Tian"
    },
    {
      "name": "Jiawei Wang"
    },
    {
      "name": "Xianfeng Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c42wtxthdvvx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14635",
  "fulltext_url": null,
  "id": "9c42wtxthdvvx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14635",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213244183",
  "pdf_url": "https://arxiv.org/pdf/2609.14635",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c42wtxthdvvx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.14635",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14635"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space",
  "title_text": "Commuting analytic and co-analytic Toeplitz operators on the harmonic Bergman space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9c42wtxthdvvx",
  "venue": "arXiv",
  "versions": []
}