{
  "id": "1301.7620",
  "version": "v1",
  "published": "2013-01-31T14:23:10.000Z",
  "updated": "2013-01-31T14:23:10.000Z",
  "title": "Order estimation of the best approximations and of the approximations by Fourier sums of classes of $(ψ,β)$--diferentiable functions",
  "authors": [
    "A. S. Serdyuk",
    "U. Z. Grabova"
  ],
  "journal": "Math.Journal. 65,No.9 (2013), p.1186-1197",
  "categories": [
    "math.CA"
  ],
  "abstract": "There were established the exact-order estimations of the best uniform approximations by{\\psi} the trigonometrical polynoms on the $C^{\\psi}_{\\beta,p}$ classes of $2\\pi$-periodic continuous functions $f$, which are defined by the convolutions of the functions, which belong to the unit ball in $L_p$, $1\\leq p <\\infty$ spaces with generating fixed kernels $\\Psi_{\\beta}\\subset|L_{p'}$, $\\frac{1}{p}+\\frac{1}{p'}=1$, whose Fourier coeficients decreasing to zero approximately as power functions. The exact order estimations were also established in $L_p$-metrics, $1 < p \\leq\\infty$ for $L^{\\psi}_{\\beta,1}$ classes of $2\\pi$-periodic functions $f$, which are equivalent by means of Lebesque measure to the convolutions of $\\Psi_{\\beta}\\subset|L_{p}$ kernels with the functions that belong to the unit ball in $L_1$ space. We showed that in investigating cases the orders of best approximations are realized by Fourier sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-31T14:23:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier sums",
      "best approximations",
      "diferentiable functions",
      "unit ball",
      "exact order estimations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.7620S"
    }
  }
}