{
  "id": "math/0310274",
  "version": "v1",
  "published": "2003-10-17T15:41:23.000Z",
  "updated": "2003-10-17T15:41:23.000Z",
  "title": "The radiation field is a Fourier integral operator",
  "authors": [
    "Antonio Sa Barreto",
    "Jared Wunsch"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We exhibit the form of the ``radiation field,'' describing the large-scale, long-time behavior of solutions to the wave equation on a manifold with no trapped rays, as a Fourier integral operator. We work in two different geometric settings: scattering manifolds (a class which includes asymptotically Euclidean spaces) and asymptotically hyperbolic manifolds. The canonical relation of the radiation field operator is a map from the cotangent bundle of the manifold to a cotangent bundle over the boundary at infinity; it is associated to a sojourn time, or Busemann function, for geodesic rays. In non-degenerate cases, the symbol of the operator can be described explicitly in terms of the geometry of long-time geodesic flow. As a consequence of the above result, we obtain a description of the (distributional) high-frequency asymptotics of the scattering-theoretic Poisson operator, better known as the Eisenstein function in the asymptotically hyperbolic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-17T15:41:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "58J45",
      "58J40",
      "58J50"
    ],
    "keywords": [
      "fourier integral operator",
      "cotangent bundle",
      "scattering-theoretic poisson operator",
      "long-time geodesic flow",
      "radiation field operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10274B"
    }
  }
}