{
  "id": "2001.00374",
  "version": "v1",
  "published": "2020-01-02T10:00:51.000Z",
  "updated": "2020-01-02T10:00:51.000Z",
  "title": "Uniform approximations by Fourier sums on classes of convolutions of periodic functions",
  "authors": [
    "A. S. Serdyuk",
    "T. A. Stepanyuk"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2\\pi$-periodic functions, which are represented by convolutions of functions $\\varphi (\\varphi\\bot 1)$ from unit ball of the space $L_{1}$ with fixed kernels $\\Psi_{\\beta}$ of the form $\\Psi_{\\beta}(t)=\\sum\\limits_{k=1}^{\\infty}\\psi(k) \\cos\\left(kt-\\frac{\\beta\\pi}{2}\\right)$, $\\sum\\limits_{k=1}^{\\infty}k\\psi(k)<\\infty$, $\\psi(k)\\geq 0$, $\\beta\\in\\mathbb{R}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-02T10:00:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier sums",
      "periodic functions",
      "uniform approximations",
      "convolutions",
      "exact upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}