{
  "id": "1810.06390",
  "version": "v1",
  "published": "2018-10-11T15:30:33.000Z",
  "updated": "2018-10-11T15:30:33.000Z",
  "title": "Heisenberg uniqueness pairs for the Fourier transform on the Heisenberg group",
  "authors": [
    "Somnath Ghosh",
    "R. K. Srivastava"
  ],
  "comment": "21 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "In this article, we prove that a non-harmonic cone is Heisenberg uniqueness pair corresponding to the unit sphere for the symplectic Fourier transform on $\\mathbb C^n.$ Further, we derive that a sphere whose radius is not contained in the zero set of the Laguerre polynomials is a determining set for the spectral projections of the finite measure supported on the unit sphere. Finally, we give a simple proof a Benedick-Amrein-Berthier type theorem for the Heisenberg group using twisted translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-11T15:30:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg group",
      "unit sphere",
      "symplectic fourier transform",
      "benedick-amrein-berthier type theorem",
      "non-harmonic cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}