{
  "abstract": "The problem of finding the extremal function of an interpolation formula and of evaluating the norm of the error functional in the Sobolev space was first posed by S.L.Sobolev. In that work (Sobolev, 1961 [1] ), the extremal function of the interpolation formula was obtained explicitly in the Sobolev space whose generalized derivatives of order m are square-integrable. The present paper considers a new optimal interpolation formula in the Sobolev space: using the discrete analog of the differential operator, we obtain the optimal coefficients of the interpolation formula for an arbitrary m , and the norm of the error functional is computed. Integration of the interpolant leads to a quadrature formula; three numerical examples confirm the theoretical order of convergence.",
  "abstract_shown": true,
  "affiliations": [
    "Tashkent State Transport University, 1, Odilkhodjaev str., Tashkent, 100167, Uzbekistan; V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., Tashkent, 100174, Uzbekistan",
    "Bukhara State University, 11, M.Ikbol str., Bukhara, 200114, Uzbekistan; Corresponding author."
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Kholmat Shadimetov"
    },
    {
      "affs": [
        1
      ],
      "name": "Khurshidjon Khayatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cccwze6awx5he.bib",
  "cited_by": 0,
  "doi": "10.1016/j.rinam.2026.100786",
  "fulltext_url": "http://www.sciencedirect.com/science/article/pii/S2590037426001044",
  "id": "cccwze6awx5he",
  "issns": [
    "2590-0374"
  ],
  "landing_url": "https://doi.org/10.1016/j.rinam.2026.100786",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7223382654",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/cccwze6awx5he.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:51Z",
      "native_id": "0ebb3b93d192429e99bbd651480b22ae",
      "source": "doaj",
      "url": "https://doi.org/10.1016/j.rinam.2026.100786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Mathematical functions and polynomials",
      "subfield": "general"
    }
  ],
  "title": "Optimal interpolation formulas in the Sobolev space of periodic functions",
  "title_text": "Optimal interpolation formulas in the Sobolev space of periodic functions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-31T14:20:26Z",
  "url": "https://research.draconitic.com/paper/cccwze6awx5he",
  "venue": "Results in Applied Mathematics",
  "versions": []
}