{
  "abstract": "We consider the problem of numerical differentiation of functions defined on the half-line: the derivative $f^{(r)}$, $ r=1,2,\\ldots$, is recovered from a finite set of perturbed Fourier--Laguerre coefficients of a function $f$, whose error is measured in $\\ell_p$, while the accuracy of approximation is measured in the uniform metric with the weight $t^αe^{-t}$. It is established that the Wiener class $W^μ_{s}$ admits such a setting for $μ>r+1-1/s$. A class of methods $\\mathcal{S}^θ$ is constructed that realize the optimal order of accuracy of numerical differentiation on $W^μ_{s}$ and use the smallest amount of input information in order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23833",
  "author_total": 2,
  "authors": [
    {
      "name": "S. G. Solodky"
    },
    {
      "name": "Y. A. Volynets"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ay10vhkxp4vfe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23833",
  "fulltext_url": null,
  "id": "ay10vhkxp4vfe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23833",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7214040903",
  "pdf_url": "https://arxiv.org/pdf/2609.23833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ay10vhkxp4vfe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23833"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Numerical differentiation of functions on the half-line in a weighted uniform metric",
  "title_text": "Numerical differentiation of functions on the half-line in a weighted uniform metric",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ay10vhkxp4vfe",
  "venue": "arXiv",
  "versions": []
}