{
  "abstract": "We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a Gabor system $\\mathcal{G}=\\mathcal{G}(g,L\\times K)\\subset \\mathbb C^N$ is block-equivalent when either the modulation set $L$ or the translation set $K$ is a subgroup of $\\mathbb Z_N$. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of $\\mathbb Z_N$ force certain diagonals of the frame operator matrix of $\\mathcal{G}$ to vanish, yielding additional sparsity and block structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.16139",
  "author_total": 3,
  "authors": [
    {
      "name": "Oleg Asipchuk"
    },
    {
      "name": "Laura De Carli"
    },
    {
      "name": "Luis Rodriguez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rq8zdpprwfrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.16139",
  "fulltext_url": null,
  "id": "6rq8zdpprwfrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.16139",
  "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": "W7161605251",
  "pdf_url": "https://arxiv.org/pdf/2605.16139",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rq8zdpprwfrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2605.16139",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.16139"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Block-equivalent finite Gabor frames",
  "title_text": "Block-equivalent finite Gabor frames",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6rq8zdpprwfrq",
  "venue": "arXiv",
  "versions": []
}