{
  "abstract": "For the Dirichlet-type space $\\mathcal D(ρ^{(1)},ρ^{(2)})$ on the unit bidisc $\\mathbb D^2,$ where $ρ^{(1)}$ and $ρ^{(2)}$ are finite positive Borel measures on the closed unit disc $\\overline{\\mathbb D},$ we show that the Lévy measure $ν_{(\\mathscr M_z,1)}$ associated with the completely alternating multisequence $\\left\\{\\|z^α\\|_{\\mathcal D(ρ^{(1)},ρ^{(2)})}^2 \\right\\}_{α\\in\\mathbb Z_+^2}$ admits the explicit representation \\begin{equation*} dν_{(\\mathscr M_z,1)}(x)=\\frac{1}{1-x_1}d((S_{*}ρ^{(1)})\\timesδ_1)(x)+\\frac{1}{1-x_2}d(δ_1\\times (S_{*}ρ^{(2)}))(x) \\end{equation*} on $[0,1]^2\\backslash\\{(1,1)\\},$ where $S_{*}ρ^{(i)},$ $i=1,2$, denotes the pushforward measure of $ρ^{(i)}$ by the map $S:\\overline{\\mathbb D}\\rightarrow [0,1]$ defined by $S(z)=|z|^2,$ $z\\in \\overline{\\mathbb D},$ and $δ_1$ denotes the Dirac measure at 1.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20346",
  "author_total": 2,
  "authors": [
    {
      "name": "Santu Bera"
    },
    {
      "name": "Shanola S. Sequeira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fytqwexj3f1rx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20346",
  "fulltext_url": null,
  "id": "fytqwexj3f1rx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20346",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7213597856",
  "pdf_url": "https://arxiv.org/pdf/2609.20346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fytqwexj3f1rx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lévy measures for Dirichlet-type spaces on the unit bidisc",
  "title_text": "Lévy measures for Dirichlet-type spaces on the unit bidisc",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fytqwexj3f1rx",
  "venue": "arXiv",
  "versions": []
}