{
  "abstract": "Let $1<p<\\infty$, let $X$ be a UMD Banach space, let $1<p<\\infty$, and let $L_d$ be the generator of the Ornstein--Uhlenbeck semigroup $(P_d(t))_{t\\geq 0}$ on $L^p(\\mathbb R^d,γ_d;X)$. We prove that the operators $-L_d$ are $R$-sectorial with a common angle strictly smaller than $π/2$ and with bounds independent of $d$. Combining this with the Hieber--Prüss transference theorem and the Kalton--Weis angle comparison, we deduce that the operators $-L_d$ admit bounded $H^\\infty$-calculi of a common angle strictly smaller than $π/2$, again with dimension-free bounds. The corresponding Walsh $R$-analyticity estimates are proved first and transferred to the Ornstein--Uhlenbeck setting by a central limit argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04974",
  "author_total": 1,
  "authors": [
    {
      "name": "Jan van Neerven"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/247bj9fx01ks6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04974",
  "fulltext_url": null,
  "id": "247bj9fx01ks6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04974",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.04974",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/247bj9fx01ks6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04974",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04974"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Dimension-free $H^\\infty$-calculus of angle $<π/2$ for UMD-valued Ornstein--Uhlenbeck operators",
  "title_text": "Dimension-free H^∞-calculus of angle <π/2 for UMD-valued Ornstein--Uhlenbeck operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/247bj9fx01ks6",
  "venue": "arXiv",
  "versions": []
}