{
  "abstract": "The aim of this paper is to establish new regions in the frame sets of Hermite functions $h_n$. A classical result of Gröchenig and Lyubarskii shows that the Gabor system $\\mathcal{G}(h_n,a\\mathbb{Z}\\times b\\mathbb{Z})$ forms a frame for $L^2(\\mathbb{R})$ whenever the lattice density exceeds $n+1$. We show that, for every $η>0$ and all sufficiently large $n$, the same Gabor system forms a frame whenever $ab\\leq n^{-\\frac{2}{3}-η}$. Moreover, we obtain an asymptotically sharp result near the coordinate axes, i.e., when one of the parameters $a$ or $b$ is small. Namely, for every $δ>0$ and $ρ\\in(0,\\frac{1}{2})$ and all sufficiently large $n$ we prove that if $\\min\\{a,b\\}\\leq n^{-\\frac{1}{2}-δ}$ and $ab\\leq \\frac{1}{2}-ρ$ then $\\mathcal{G}(h_n,a\\mathbb{Z}\\times b\\mathbb{Z})$ forms a frame.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01296",
  "author_total": 3,
  "authors": [
    {
      "name": "Markus Faulhuber"
    },
    {
      "name": "Irina Shafkulovska"
    },
    {
      "name": "Ilya Zlotnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7aasgzsvhmjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01296",
  "fulltext_url": null,
  "id": "e7aasgzsvhmjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01296",
  "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.CA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7206161211",
  "pdf_url": "https://arxiv.org/pdf/2609.01296",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7aasgzsvhmjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.01296",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01296"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic safety regions for Gabor frames generated by Hermite functions",
  "title_text": "Asymptotic safety regions for Gabor frames generated by Hermite functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/e7aasgzsvhmjz",
  "venue": "arXiv",
  "versions": []
}