{
  "abstract": "Let $d_k>0$ and let $Q_k$ be a polynomial of degree $r_k$ with nonnegative Chebyshev coefficients. We study locally uniform limits of $f_k(z)=C_kQ_k(\\cos(d_kz))$, where $C_k>0$. If $f_k\\to F$ locally uniformly and $F(0)>0$, the associated positive lattice measures converge weakly, their second moments converge, and their quadratic tails are uniformly integrable. If additionally all zeros of $Q_k$ lie in $[-1,1)$, $d_k\\to0$, and $F$ has order below two, then for every $A>0$ with $F(A)F(-A)\\ne0$, $\\limsup_{k\\to\\infty} r_kd_k^2\\le 4\\sum_{γ_n>A}γ_n^{-2}$, where $\\{\\pmγ_n\\}$ are the nonzero real zeros of $F$, counted with multiplicity. If, moreover, $f_k\\to F$ locally uniformly with $F(0)>0$, all zeros of $Q_k$ lie in $[-1,1)$, and $F$ has no nonzero real period, has order below two, and is not of finite exponential type, then $d_k\\to0$, $r_kd_k\\to\\infty$, and $r_kd_k^2\\to0$. Equivalently, $d_k^{-1}=o(r_k)$ and $r_k=o(d_k^{-2})$. Boundary examples show the role of the hypotheses and the Gaussian boundary at order two.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28792",
  "author_total": 1,
  "authors": [
    {
      "name": "Vasily Stodolsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5845trejpmce1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28792",
  "fulltext_url": null,
  "id": "5845trejpmce1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28792",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7204864368",
  "pdf_url": "https://arxiv.org/pdf/2608.28792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5845trejpmce1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.28792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Mesh-Degree Rigidity for Positive Chebyshev-Fourier Approximants",
  "title_text": "Mesh-Degree Rigidity for Positive Chebyshev-Fourier Approximants",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/5845trejpmce1",
  "venue": "arXiv",
  "versions": []
}