{
  "id": "1006.5310",
  "version": "v1",
  "published": "2010-06-28T10:39:52.000Z",
  "updated": "2010-06-28T10:39:52.000Z",
  "title": "Uniqueness of solutions to the Schrodinger equation on the Heisenberg group",
  "authors": [
    "Salem Ben Said",
    "Sundaram Thangavelu"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "This paper deals with the Schr{\\\"o}dinger equation $i\\partial_s u({\\bf z},t;s)-\\cal L u({\\bf z}, t;s)=0,$ where $\\cal L$ is the sub-Laplacian on the Heisenberg group. Assume that the initial data $f$ satisfies $| f({\\bf z},t)| \\leq C q_a({\\bf z},t),$ where $q_s$ is the heat kernel associated to $\\cal L.$ If in addition $ |u({\\bf z},t;s_0)|\\leq C q_b({\\bf z},t),$ for some $s_0\\in \\R^*,$ then we prove that $u({\\bf z},t;s)=0$ for all $s\\in \\R $ whenever $ab<s_0^2.$ This result also holds true on $H$-type groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-28T10:39:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg group",
      "schrodinger equation",
      "uniqueness",
      "holds true",
      "paper deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.5310B"
    }
  }
}