{
  "abstract": "In this paper we present results related to Donoho--Stark type uncertainty principles that were proved in the article \"The uncertainty principle: variations on a theme\" by Wigderson and Wigderson for $k$-Hadamard operators in the finite-dimensional setting. Namely, the authors showed that Donoho-Stark principles can be generalized to versions for approximate supports with respect to norms $\\ell^{p}$ for $p=1$ and $p=2$. In the second case they assumed the so-called speciality condition, namely that a suitable matrix satisfies $A^{*}A = kI$. First we show that such theorems cannot be generalized to $p>1$ if matrices are not special $k$-Hadamard. Next we prove Donoho-Stark type principle for special $k$-Hadamard operators for $\\ell^{p}$ norms within the range $1\\leq p\\leq 2$. Finally, we show that such theorems are false for $p>2$ even in the presence of the speciality condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41902",
  "author_total": 1,
  "authors": [
    {
      "name": "Rami Ayoush"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8v5p5mnec3235.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41902",
  "fulltext_url": null,
  "id": "8v5p5mnec3235",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41902",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8v5p5mnec3235.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On approximate support versions of Donoho--Stark uncertainty principles for $k$-Hadamard operators",
  "title_text": "On approximate support versions of Donoho--Stark uncertainty principles for k-Hadamard operators",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/8v5p5mnec3235",
  "venue": "arXiv",
  "versions": []
}