{
  "abstract": "We prove the exact asymptotics of the multidimensional normalized $L^1$ Nikolskii constant \\[ \\mathcal L^*(d)=\\Bigl(\\fracπ{2}+o(1)\\Bigr)2^{-d}, \\quad d\\to\\infty. \\] In addition, for each fixed dimension we obtain asymptotics for the positive zeros of the extremal function $φ_d$, and determine their limiting distribution as $d\\to\\infty$. The lower bound follows from the construction of an admissible function and its asymptotic analysis. For the upper bound, we represent $x^{d+1}φ_d(x)$ as the product of two solutions of the equation $u''+V_d(x)u=0$, compare this equation with a Bessel model, and analyze relative canonical products.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06240",
  "author_total": 1,
  "authors": [
    {
      "name": "D. V. Gorbachev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7mjw57pp9hn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06240",
  "fulltext_url": null,
  "id": "a7mjw57pp9hn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06240",
  "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.CA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7211991378",
  "pdf_url": "https://arxiv.org/pdf/2609.06240",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7mjw57pp9hn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06240",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06240"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Exact Asymptotics of the Multidimensional Nikolskii Constant",
  "title_text": "Exact Asymptotics of the Multidimensional Nikolskii Constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/a7mjw57pp9hn9",
  "venue": "arXiv",
  "versions": []
}