{
  "id": "1806.07880",
  "version": "v1",
  "published": "2018-06-20T08:48:39.000Z",
  "updated": "2018-06-20T08:48:39.000Z",
  "title": "On the uncertainty product of spherical functions",
  "authors": [
    "Ilona Iglewska-Nowak"
  ],
  "comment": "22 pages",
  "categories": [
    "math.CA",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The uncertainty product of a function is a quantity that measures the trade-off between the space and the frequency localization of the function. Its boundedness from below is the content of various uncertainty principles. In the present paper, functions over the $n$-dimensional sphere are considered. A formula is derived that expresses the uncertainty product of a continuous function in terms of its Fourier coefficients. It is applied to a directional derivative of a zonal wavelet, and the behavior of the uncertainty product of this function is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-20T08:48:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42C40",
      "42A63"
    ],
    "keywords": [
      "uncertainty product",
      "spherical functions",
      "zonal wavelet",
      "uncertainty principles",
      "dimensional sphere"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}