{
  "id": "0911.4582",
  "version": "v2",
  "published": "2009-11-24T17:15:43.000Z",
  "updated": "2010-02-01T15:54:08.000Z",
  "title": "Spherical means with centers on a hyperplane in even dimensions",
  "authors": [
    "E K Narayanan",
    "Rakesh"
  ],
  "comment": "Revised version. Corrected some typing errors and added a figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a real valued function on R^n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-01T15:54:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35L15",
      "35R30",
      "44A05",
      "44A12",
      "92C55"
    ],
    "keywords": [
      "spherical means",
      "inversion formula",
      "hyperplane",
      "dimensions",
      "fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4582N"
    }
  }
}