{
  "id": "2005.03607",
  "version": "v1",
  "published": "2020-05-07T17:07:59.000Z",
  "updated": "2020-05-07T17:07:59.000Z",
  "title": "The Fourier Transform Approach to Inversion of lambda-Cosine and Funk Transforms on the Unit Sphere",
  "authors": [
    "Boris Rubin"
  ],
  "comment": "14 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained for totally geodesic Funk transforms on the sphere and the correpsonding lambda-cosine transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-07T17:07:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A12"
    ],
    "keywords": [
      "fourier transform approach",
      "unit sphere",
      "totally geodesic funk transforms",
      "usual beltrami-laplace operator",
      "analytic families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}