{
  "id": "1405.0444",
  "version": "v1",
  "published": "2014-05-02T16:18:39.000Z",
  "updated": "2014-05-02T16:18:39.000Z",
  "title": "On One Problem of Optimization of Approximate Integration",
  "authors": [
    "V. F. Babenko"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "It is proved that interval quadrature formula of the form $$ q(f)=\\sum\\limits_{k=1}^nc_k\\frac 1{2h}\\int\\limits_{x_k-h}^{x_k+h}f(t)dt $$ ($c_k\\in \\RR, \\, x_1+h<x_2-h<x_2+h<...<x_n-h<x_n+h<x_1+2\\pi -h$) with equal $c_k$ and equidistant $x_k$ is optimal among all such formulas for the class $K*F_1$ of convolutions of a $CVD$-kernel $K$ with functions from the unite ball of the space $L_1$ of $2\\pi$-periodic integrable functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-02T16:18:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "approximate integration",
      "optimization",
      "interval quadrature formula",
      "periodic integrable functions",
      "unite ball"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0444B"
    }
  }
}