{
  "annotation_id": "de28f60a-04fc-446e-9a28-552d40905455",
  "date_created": "2026-02-17T05:53:11.626000Z",
  "date_modified": "2026-02-17T05:53:11.626000Z",
  "file_hash": "4edc503e8919d03f1002e01ef8c90cb2102108f845c31553e80380739fd439aa",
  "private": false,
  "record": {
    "abstract": "We exhibit a new infinite family of hyperbolic curves in the complement of the frame set of Gabor systems with B-spline generators. The proof technique is a combination of an approach by Gr\\\"ochenig [Partitions of unity and new obstructions for Gabor frames, arXiv:1507.08432, 2015] and a partly partition of unity argument by Nielsen and the author [Counterexamples to the B-spline conjecture for Gabor frames, J. Fourier Anal. Appl., 22(6):1440-1451, 2016]. We relate the new hyperbolic obstructions to the \"right bow tie\" of the so-called Janssen tie [Zak transforms with few zeros and the tie, In Advances in Gabor analysis, Birkh\\\"auser, 2003].",
    "arxiv_id": "2601.07642",
    "authors": [
      "Jakob Lemvig"
    ],
    "categories": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "A new family of hyperbolic slits in the Gabor frame set of B-spline generators",
    "url": "https://arxiv.org/abs/2601.07642",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9d192ebe-07b3-4e81-aae4-204b9f6ee7ab",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}