{
  "id": "1507.02624",
  "version": "v1",
  "published": "2015-07-08T15:04:42.000Z",
  "updated": "2015-07-08T15:04:42.000Z",
  "title": "Non-harmonic cones are Heisenberg uniqueness pairs for the Fourier transform on $\\mathbb R^n$",
  "authors": [
    "R. K. Srivastava"
  ],
  "comment": "9 pages. arXiv admin note: substantial text overlap with arXiv:1506.07425",
  "categories": [
    "math.CA"
  ],
  "abstract": "A Heisenberg uniqueness pair is a pair $\\left(\\Gamma, \\Lambda\\right)$, where $\\Gamma$ is a surface and $\\Lambda\\subset\\mathbb R^n$ be such that any finite Borel measure $\\mu$ which is supported on $\\Gamma$ and absolutely continuous with respect to the surface measure, whose Fourier transform $\\widehat\\mu$ vanishes on $\\Lambda,$ implies $\\mu=0.$ In this article, we prove that a cone is a Heisenberg uniqueness pair corresponding to the unit sphere as long as it does not completely lay on the level surface of any homogeneous harmonic polynomial on $\\mathbb R^n.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-08T15:04:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fourier transform",
      "non-harmonic cones",
      "finite borel measure",
      "surface measure",
      "homogeneous harmonic polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150702624S"
    }
  }
}