{
  "id": "1310.6831",
  "version": "v1",
  "published": "2013-10-25T06:43:29.000Z",
  "updated": "2013-10-25T06:43:29.000Z",
  "title": "The discrete analogue of the differential operator $\\frac{d^{2m}}{d x^{2m}} + 2ω^2\\frac{d^{2m-2}}{d x^{2m-2}} + ω^4\\frac{d^{2m-4}}{d x^{2m-4}}$",
  "authors": [
    "A. R. Hayotov"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In the present paper we construct the discrete analogue $D_m(h\\beta)$ of the differential operator $\\frac{d^{2m}}{d x^{2m}} + 2\\omega^2\\frac{d^{2m-2}}{d x^{2m-2}} + \\omega^4\\frac{d^{2m-4}}{d x^{2m-4}}$. The discrete analogue $D_m(h\\beta)$ plays the main role in construction of optimal quadrature formulas and interpolation splines minimizing the semi-norm in the $K_2(P_m)$ Hilbert space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-25T06:43:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete analogue",
      "differential operator",
      "optimal quadrature formulas",
      "main role",
      "hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.6831H"
    }
  }
}