{
  "id": "1906.02531",
  "version": "v1",
  "published": "2019-06-06T11:44:17.000Z",
  "updated": "2019-06-06T11:44:17.000Z",
  "title": "Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness",
  "authors": [
    "A. S. Serdyuk",
    "I. V. Sokolenko"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\\beta,p}, 1\\le p\\le\\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\\rightarrow\\infty)$ in the uniform metric. We obtain similar estimates for approximations of the classes $W^r_{\\beta,1}$ in metrics of the spaces $L_p, 1\\le p\\le\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-06T11:44:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A10"
    ],
    "keywords": [
      "fourier sums",
      "high exponents",
      "differentiable functions",
      "approximation",
      "smoothness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}