{
  "abstract": "Let $H$ be an infinite-dimensional Hilbert space and let $\\set{x_n}\\inN$ be a frame for $H$. We say that a sequence $\\set{y_n}\\inN$ is an \\emph{alternative dual} of $\\set{x_n}\\inN$ if $$x=\\sumli\\ip{x}{y_n}x_n\\quad \\text{for all }x\\in H,$$ with the convergence of the series in the norm of $H.$ We say that a sequence $\\set{z_n}\\inN$ is a \\emph{pseudo-synthesis dual} of $\\set{x_n}\\inN$ if $$x=\\sumli\\ip{x}{x_n}z_n \\quad \\text{for all }x\\in H,$$ with the convergence of the series in the norm of $H.$ We prove that, at every level of smoothness of the generator, there exist Gabor frames for $L^2(\\R^d)$ with infinitely many alternative duals (and pseudo-synthesis duals) such that none of them is a Gabor system",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32246",
  "author_total": 1,
  "authors": [
    {
      "name": "Pu-Ting Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3h6yk4qd4rq0z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32246",
  "fulltext_url": null,
  "id": "3h6yk4qd4rq0z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32246",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
  ],
  "openalex": "W7214752762",
  "pdf_url": "https://arxiv.org/pdf/2609.32246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3h6yk4qd4rq0z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gabor frames with no Gabor duals",
  "title_text": "Gabor frames with no Gabor duals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3h6yk4qd4rq0z",
  "venue": "arXiv",
  "versions": []
}