{
  "id": "math-ph/0408022",
  "version": "v1",
  "published": "2004-08-12T10:50:37.000Z",
  "updated": "2004-08-12T10:50:37.000Z",
  "title": "Uniqueness in the Characteristic Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions",
  "authors": [
    "Peter Ullrich"
  ],
  "comment": "19 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a ``tame'' restriction to the characteristic (hyper)surface $\\{x^0+x^n=0\\}$ in $(1+n)$-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space $\\cS'_{\\partial_-}(\\R^n)$ which we have introduced in \\cite{PullJMP}. Moreover, we show that every element of $\\cS'_{\\partial_-}(\\R^n)$ appears as the ``tame'' restriction of a solution of the (homogeneous) Klein-Gordon equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-12T10:50:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L15",
      "35D05"
    ],
    "keywords": [
      "klein-gordon equation",
      "characteristic cauchy problem",
      "tame restrictions",
      "generalized functions",
      "uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.ph...8022U"
    }
  }
}