{
  "abstract": "We determine the best constants in estimates of the $L^\\infty$ norm of functions on the sphere with bounded Laplacian whose first spherical harmonic components vanish. In every dimension $d\\geq2$, these constants are expressed through weighted $L^1$ extremal polynomials. On $S^2$ the constant is an explicit positive series, and the best coefficient of $n^{-2}$ is $7ζ(3)/4$. On $S^3$ the best coefficient of $n^{-2}$ is a positive integral involving the Hörmander--Bernhardsson extremal function. In higher dimensions the rescaled extremal polynomials converge to weighted entire extremals, which give asymptotic formulas for the Bohr constants on $S^4$ and $S^6$. The most unexpected and, in our view, interesting observation is that, for every fixed $n\\geq2$ on $S^2$ and $S^3$, the constants in best approximation estimates are \\emph{strictly smaller} than the corresponding Bohr--Favard constants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14811",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexey Solyanik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3kknxwh6fzj2q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14811",
  "fulltext_url": null,
  "id": "3kknxwh6fzj2q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14811",
  "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-ph"
    ],
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7221798485",
  "pdf_url": "https://arxiv.org/pdf/2610.14811",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3kknxwh6fzj2q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.14811",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14811"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On best approximation and estimates of Bohr--Favard type on the sphere for functions with bounded Laplacian",
  "title_text": "On best approximation and estimates of Bohr--Favard type on the sphere for functions with bounded Laplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3kknxwh6fzj2q",
  "venue": "arXiv",
  "versions": []
}