{
  "id": "1305.4374",
  "version": "v1",
  "published": "2013-05-19T15:45:49.000Z",
  "updated": "2013-05-19T15:45:49.000Z",
  "title": "Estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions",
  "authors": [
    "A. S. Serdyuk",
    "U. Z. Grabova"
  ],
  "comment": "17 pages, in Ukrainian",
  "journal": "Zb. Pr. Inst. Mat. NAN Ukr. 10, No 1 (2013), p. 222-244",
  "categories": [
    "math.CA"
  ],
  "abstract": "We obtain order-exact estimates for uniform approximations by using Zygmund sums $Z^{s}_{n}$ of classes $C^{\\psi}_{\\beta,p}$ of $2\\pi$-periodic continuous functions $f$ representable by convolutions of functions from unit balls of the space $L_{p}$, $1< p<\\infty$, with a fixed kernels $\\Psi_{\\beta}\\in L_{p'}$, $\\frac{1}{p}+\\frac{1}{p'}=1$. In addition, we find a set of allowed values of parameters (that define the class $C^{\\psi}_{\\beta,p}$ and the linear method $Z^{s}_{n}$) for which Zygmund sums and Fejer sums realize the order of the best uniform approximations by trigonometric polynomials of those classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-19T15:45:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zygmund sums",
      "periodic functions",
      "convolutions",
      "best uniform approximations",
      "periodic continuous functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4374S"
    }
  }
}