{
  "id": "0711.1897",
  "version": "v1",
  "published": "2007-11-13T00:58:01.000Z",
  "updated": "2007-11-13T00:58:01.000Z",
  "title": "Spherical Means in Odd Dimensions and EPD equations",
  "authors": [
    "Boris Rubin"
  ],
  "categories": [
    "math.FA",
    "math.AP"
  ],
  "abstract": "The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux equation with initial data on the cylindrical surface. The argument relies on the idea of analytic continuation and known properties of Erdelyi-Kober fractional integrals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-13T00:58:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "44A12",
      "92C55",
      "65R32"
    ],
    "keywords": [
      "odd dimensions",
      "epd equations",
      "erdelyi-kober fractional integrals",
      "finch-patch-rakesh inversion formula",
      "spherical mean radon transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1897R"
    }
  }
}