{
  "id": "1404.5656",
  "version": "v1",
  "published": "2014-04-22T21:32:35.000Z",
  "updated": "2014-04-22T21:32:35.000Z",
  "title": "Estimates of the best approximations and approximations of Fourier sums of classes of convolutions of periodic functions of not high smoothness in integral metrics",
  "authors": [
    "T. A. Stepaniuk"
  ],
  "comment": "23 pages, in Ukrainian",
  "categories": [
    "math.CA"
  ],
  "abstract": "In metric of spaces $L_{s}, \\ 1< s\\leq\\infty$, we obtain exact order estimates of best approximations and approximations by Fourier sums of classes of convolutions the periodic functions that belong to unit ball of space $L_{1}$, with generating kernel $\\Psi_{\\beta}(t)=\\sum\\limits_{k=1}^{\\infty}\\psi(k)\\cos(kt-\\frac{\\beta\\pi}{2})$, $\\beta\\in\\mathbb{R}$, whose coefficients $\\psi(k)$ are such that product $\\psi(n)n^{1-\\frac{1}{s}}$, $1<s\\leq\\infty$, can't tend to nought faster than every power function and besides, if $1<s<\\infty$, then $\\sum\\limits_{k=1}^{\\infty}\\psi^{s}(k)k^{s-2}<\\infty$ and if $s=\\infty$, then $\\sum\\limits_{k=1}^{\\infty}\\psi(k)<\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-22T21:32:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "best approximations",
      "fourier sums",
      "periodic functions",
      "high smoothness",
      "integral metrics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5656S"
    }
  }
}