{
  "abstract": "We study the zero sets of the Zak transform $Z_λB_n(x,ν)$ of B-splines for $λ> 0$. Specifically, we provide a full characterization of the zero set for the hat spline for all positive values of the parameter $λ$ and for higher order B-splines when $λ> 1$. Finally, we apply these results to establish the frame property of integer-oversampled Gabor systems generated by B-splines. In particular, we characterize the frame property for integer-oversampled Gabor systems generated by the hat splines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13116",
  "author_total": 2,
  "authors": [
    {
      "name": "Marzieh Hasannasab"
    },
    {
      "name": "Jakob Lemvig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/88388mkcrhx77.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13116",
  "fulltext_url": null,
  "id": "88388mkcrhx77",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13116",
  "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|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7212476608",
  "pdf_url": "https://arxiv.org/pdf/2609.13116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/88388mkcrhx77.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13116"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The zero set of the Zak transform of B-splines with applications to Gabor frames",
  "title_text": "The zero set of the Zak transform of B-splines with applications to Gabor frames",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/88388mkcrhx77",
  "venue": "arXiv",
  "versions": []
}