{
  "abstract": "We establish sharp sampling and interpolation criteria for the radial--angular Gaussian mixed-norm Fock spaces $\\mathcal F_α^{p,q}$, where $α>0$ and $0<p,q\\le\\infty$. The natural point-evaluation scale leads to the normalized restriction $R_{α,Λ}^{p,q}f = \\bigl(f(λ)e^{-\\fracα{2}|λ|^2}(1+|λ|)^{\\frac{1}{q}-\\frac{1}{p}}\\bigr)_{λ\\inΛ}$. With this normalization, the critical density is the classical value $\\fracαπ$ throughout the Banach and quasi-Banach ranges. For an arbitrary locally finite set $Λ$, sampling is equivalent to $D_{\\mathrm{sep}}^{-}(Λ)>\\fracαπ$, together with relative separation when $p<\\infty$; no relative-separation condition is required when $p=\\infty$. Here $D_{\\mathrm{sep}}^{-}$ is the supremum of the lower Beurling densities over separated subsets of $Λ$. Interpolation is equivalent to separation and $D^{+}(Λ)<\\fracαπ$. The same criterion characterizes interpolation for the little endpoint $f_α^{p,\\infty}$, and in both settings the normalized restriction map admits a bounded linear right inverse. The sufficiency arguments are based on rapidly localized Hilbert dual and Lagrange atoms together with a weighted localized synthesis theorem on the full mixed-norm scale. For necessity, we prove that lower stability of a rapidly localized matrix on a weighted annular mixed sequence space implies lower stability on $\\ell^2$. The proof first passes to $\\ell^\\infty$ by translated polynomial cutoffs and a commutator estimate, and then uses the $p$-independence theorem for the Sjöstrand class. Applied through a fixed Hilbert sampling lattice, this reduces the strict density conditions to the classical Hilbert Fock sampling and interpolation theorems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23572",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiang Fang"
    },
    {
      "name": "Pham Trong Tien"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ffq2hya5f6t7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23572",
  "fulltext_url": null,
  "id": "ffq2hya5f6t7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23572",
  "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.CV"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214002445",
  "pdf_url": "https://arxiv.org/pdf/2609.23572",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ffq2hya5f6t7w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23572",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23572"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sampling and Interpolation in Gaussian Mixed-Norm Fock Spaces",
  "title_text": "Sampling and Interpolation in Gaussian Mixed-Norm Fock Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ffq2hya5f6t7w",
  "venue": "arXiv",
  "versions": []
}