{
  "abstract": "We extend certain results of the theory of Fourier quasicrystals on the real line to the case of a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform for measures on the line. We consider positive or translation bounded measures $μ$ on a strip whose Fourier transform is a pure point measure $\\hatμ=\\sum_{γ\\inΓ}b_γδ_γ$ (as usual, $δ_γ$ is the unit mass at the point $γ$). We prove that the measure $ν=\\sum_{γ\\inΓ}|b_γ|^2δ_γ$ has the exponential growth. Moreover, if for some $η>0$ the points of $Γ$ in every interval of length $η$ are linearly independent over integers, then the measure $\\hatμ$ also has the exponential growth.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.10766",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergii Favorov"
    },
    {
      "name": "Özkan Deǧer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2tnzcfgx4yyx4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.10766",
  "fulltext_url": null,
  "id": "2tnzcfgx4yyx4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.10766",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.10766",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2tnzcfgx4yyx4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2605.10766",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.10766"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Some properties of Fourier quasicrystals and measures on a strip",
  "title_text": "Some properties of Fourier quasicrystals and measures on a strip",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/2tnzcfgx4yyx4",
  "venue": "arXiv",
  "versions": []
}