{
  "abstract": "We give a complete characterization of the zero set of the Zak transform of the second-order B-spline $Q_2$. As a consequence, we obtain a new proof of the Lemvig--Nielsen obstructions to the Gabor frame property of $Q_2$, and, along the hyperbola $ab=1/q$, we show these obstructions are sharp: every point they do not exclude belongs to the frame set. This gives the first complete characterization of $\\mathcal F(Q_2)$ along an entire curve in this family, resolving a question left open by Lemvig and Nielsen.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00481",
  "author_total": 2,
  "authors": [
    {
      "name": "Alexander Stangl"
    },
    {
      "name": "Christina Frederick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7bcr39hszs6fq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00481",
  "fulltext_url": null,
  "id": "7bcr39hszs6fq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00481",
  "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"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7206207958",
  "pdf_url": "https://arxiv.org/pdf/2609.00481",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7bcr39hszs6fq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.00481",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00481"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The frameset of the second-order B-Spline along $ab=1/q$",
  "title_text": "The frameset of the second-order B-Spline along ab=1/q",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/7bcr39hszs6fq",
  "venue": "arXiv",
  "versions": []
}