{
  "abstract": "We prove a refinement of Jackson's theorem on the approximation of Lipschitz functions by trigonometric polynomials. Our result precisely characterizes the leading error term associated with Jackson's construction. We do the same for a related construction commonly used in the kernel polynomial method for spectral density estimation, which is slightly better than Jackson's construction in this respect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.23375",
  "author_total": 3,
  "authors": [
    {
      "name": "Rikhav Shah"
    },
    {
      "name": "John Urschel"
    },
    {
      "name": "Nicholas West"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28dq5sm3xtzde.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23375",
  "fulltext_url": null,
  "id": "28dq5sm3xtzde",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23375",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.23375",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28dq5sm3xtzde.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.23375",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23375"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "What is Jackson's constant?",
  "title_text": "What is Jackson's constant?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/28dq5sm3xtzde",
  "venue": "arXiv",
  "versions": []
}