{
  "id": "2006.08147",
  "version": "v1",
  "published": "2020-06-15T06:02:13.000Z",
  "updated": "2020-06-15T06:02:13.000Z",
  "title": "Toeplitz matrices for the study of the fractional Laplacian on a bounded interval",
  "authors": [
    "Philippe Rambour",
    "Abdellatif Seghier"
  ],
  "categories": [
    "math.CA",
    "math.FA",
    "math.OA"
  ],
  "abstract": "Toeplitz matrices for the study of the fractional Laplacian on a bounded interval. In this work we get a deep link between (--$\\Delta$) $\\alpha$ ]0,1[ the fractional Laplacian on the interval ]0, 1[ and T N ($\\Phi$ $\\alpha$) the Toeplitz matrices of symbol $\\Phi$ $\\alpha$ : $\\theta$ $\\rightarrow$ |1 -- e i$\\theta$ | 2$\\alpha$ when N goes to the infinity and for $\\alpha$ $\\in$]0, 1 2 [$\\cup$] 1 2 , 1[. In the second part of the paper we provide a Green function for the fractional equation (--$\\Delta$) $\\alpha$ ]0,1[ ($\\psi$) = f for $\\alpha$ $\\in$]0, 1 2 [ and f a sufficiently smooth function on [0, 1]. The interest is that this Green's function is the same as the Laplacian operator of order 2n, n $\\in$ N. Mathematical Subject Classification (2000) Primary 35S05, 35S10,35S11 ; Secondary 47G30.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-15T06:02:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional laplacian",
      "toeplitz matrices",
      "bounded interval",
      "greens function",
      "second part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}