{
  "abstract": "We investigate the spectral and boundedness properties of the inverse Ornstein--Uhlenbeck operator $\\mathcal{A}^{Q,B}$ and its associated semigroup in $L^p$ spaces with respect to the inverse Gaussian measure. We establish strong continuity and contractivity of this semigroup in $L^p$ for $p \\in [1, \\infty)$, and obtain a complete characterization of the spectrum of $\\mathcal{A}^{Q,B}$. For $p \\in (1, \\infty)$, the spectrum is independent of $p$, consists entirely of eigenvalues and exhibits a spectral gap. For $p=1$, the spectrum is instead the left half-plane. Furthermore, we discuss ultracontractivity and hypercontractivity properties of the semigroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06826",
  "author_total": 4,
  "authors": [
    {
      "name": "Tommaso Bruno"
    },
    {
      "name": "Valentina Casarino"
    },
    {
      "name": "Paolo Ciatti"
    },
    {
      "name": "Peter Sjögren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ff8sr4b9qndhk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06826",
  "fulltext_url": null,
  "id": "ff8sr4b9qndhk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06826",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ff8sr4b9qndhk.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06826"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spectral and mapping properties of the inverse Ornstein--Uhlenbeck operator",
  "title_text": "Spectral and mapping properties of the inverse Ornstein--Uhlenbeck operator",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/ff8sr4b9qndhk",
  "venue": "arXiv",
  "versions": []
}