{
  "id": "1112.5469",
  "version": "v4",
  "published": "2011-12-22T21:36:59.000Z",
  "updated": "2013-02-18T14:38:20.000Z",
  "title": "On Fourier transforms of radial functions and distributions",
  "authors": [
    "Loukas Grafakos",
    "Gerald Teschl"
  ],
  "comment": "12 pages",
  "journal": "J. Fourier Anal. Appl. 19, 167-179 (2013)",
  "doi": "10.1007/s00041-012-9242-5",
  "categories": [
    "math.CA",
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We find a formula that relates the Fourier transform of a radial function on $\\mathbf{R}^n$ with the Fourier transform of the same function defined on $\\mathbf{R}^{n+2}$. This formula enables one to explicitly calculate the Fourier transform of any radial function $f(r)$ in any dimension, provided one knows the Fourier transform of the one-dimensional function $t\\to f(|t|)$ and the two-dimensional function $(x_1,x_2)\\to f(|(x_1,x_2)|)$. We prove analogous results for radial tempered distributions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-02-18T14:38:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "42A10",
      "42B37"
    ],
    "keywords": [
      "fourier transform",
      "radial function",
      "formula enables",
      "one-dimensional function",
      "two-dimensional function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5469G"
    }
  }
}