{
  "abstract": "Consider the compressed shift $T=P_{K_θ}M_z|_{K_θ}$ on $K_θ=H^2\\ominusθH^2$ associated with the atomic singular inner function $θ(z)=\\exp(-a(ζ+z)/(ζ-z))$, $a>0$ and $|ζ|=1$. Let $k_0=P_{K_θ}1$ and define real powers $T^s$ using a holomorphic logarithm near the singleton spectrum of $T$. For any temporal multisequence $\\mathsf S=(s_k)_{k\\in I}\\subset[0,\\infty)$ with uniformly bounded numbers of samples in unit intervals, we prove that $\\{T^{s_k}k_0:k\\in I\\}$ is a frame if and only if $\\mathsf S$ is Kummer-thick: the frequencies $ω(s_k)=\\sqrt{8s_k+4}$, weighted by $1/ω(s_k)$, have uniformly positive total mass in every sufficiently distant interval of some fixed length. Equivalently, the occupied unit cells fill a fixed positive proportion of every window $[N-C\\sqrt N,N+C\\sqrt N]$ for some $C>0$ and all sufficiently large $N$. The proof combines a Volterra transmutation into Bessel waves with the Fourier--Bessel Logvinenko--Sereda theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27255",
  "author_total": 2,
  "authors": [
    {
      "name": "Ilya Krishtal"
    },
    {
      "name": "Javad Mashreghi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej7p16z1q5cjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27255",
  "fulltext_url": null,
  "id": "ej7p16z1q5cjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27255",
  "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": "W7214221208",
  "pdf_url": "https://arxiv.org/pdf/2609.27255",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej7p16z1q5cjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27255",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27255"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Mesoscopic redundancy for dynamical frames generated by atomic singular model operators",
  "title_text": "Mesoscopic redundancy for dynamical frames generated by atomic singular model operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/ej7p16z1q5cjz",
  "venue": "arXiv",
  "versions": []
}