{
  "id": "2202.03113",
  "version": "v1",
  "published": "2022-02-07T12:46:53.000Z",
  "updated": "2022-02-07T12:46:53.000Z",
  "title": "Approximation by Fourier sums in classes of Weyl--Nagy differentiable functions with high exponent of smoothness",
  "authors": [
    "A. S. Serdyuk",
    "I. V. Sokolenko"
  ],
  "comment": "16 pages, in Russian language",
  "categories": [
    "math.CA"
  ],
  "abstract": "We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order $n-1$ of classes of $2\\pi$-periodic Weyl--Nagy differentiable functions, $W^r_{\\beta,p}, 1\\le p\\le \\infty, \\beta\\in\\mathbb{R},$ for high exponents of smoothness $r\\ (r-1\\ge \\sqrt{n})$. We obtain similar estimates in metrics of the spaces $L_p, 1\\le p\\le\\infty,$ for functional classes $W^r_{\\beta,1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-07T12:46:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier sums",
      "high exponent",
      "approximation",
      "smoothness",
      "periodic weyl-nagy differentiable functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "ru",
      "license": "arXiv",
      "status": "editable"
    }
  }
}