{
  "abstract": "We study Gaussian integral operators \\[(Tf)(z)=\\frac1π\\int_{\\mathbb C} e^{αz^2+β\\overline w^{\\,2}+γz\\overline w+ηz+δ\\overline w} f(w)e^{-|w|^2}\\,dA(w)\\] acting between Fock spaces $\\mathcal F^p$ and $\\mathcal F^q$, where $0<p,q\\leq\\infty$. We give complete characterizations of their boundedness and compactness in terms of explicit conditions on the parameters of the Gaussian kernel. The proofs are based on a unified approach combining reproducing-kernel estimates, atomic decompositions, and sampling sequences, together with a reduction to diagonal operators on sequence spaces. We also study Schatten-class membership on $\\mathcal F^2$ and compute the Hilbert--Schmidt norm explicitly.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28279",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuanqi Sang"
    },
    {
      "name": "Liankuo Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h06xkdn1n95g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28279",
  "fulltext_url": null,
  "id": "4h06xkdn1n95g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28279",
  "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": "W7223084137",
  "pdf_url": "https://arxiv.org/pdf/2610.28279",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h06xkdn1n95g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28279",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28279"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gaussian Integral Operator between Fock Spaces",
  "title_text": "Gaussian Integral Operator between Fock Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/4h06xkdn1n95g",
  "venue": "arXiv",
  "versions": []
}