{
  "id": "2102.07551",
  "version": "v1",
  "published": "2021-02-15T13:41:00.000Z",
  "updated": "2021-02-15T13:41:00.000Z",
  "title": "Optimal quadrature formulas for computing of Fourier integrals in a Hilbert space",
  "authors": [
    "A. R. Hayotov",
    "S. S. Babaev"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2001.02636",
  "journal": "Problems of Computational and Applied Mathematics, 2020",
  "categories": [
    "math.NA",
    "cs.NA",
    "math.CV"
  ],
  "abstract": "In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\\int_a^b e^{2\\pi i\\omega x}\\varphi(x)d x$ with $\\omega\\in \\mathbb{R}$ in the Hilbert space $W_2^{(2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-15T13:41:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert space",
      "fourier integrals",
      "constructed optimal quadrature formulas",
      "explicit expressions",
      "complex-valued functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}