ar X iv : m at h / 03 12 10 8 v 1 [ m at h . A P ] 4 D ec 2 00 3 RADIATION FIELDS , SCATTERING AND INVERSE SCATTERING ON ASYMPTOTICALLY HYPERBOLIC MANIFOLDS

نویسنده

  • ANTÔNIO SÁ
چکیده

In analogy with radiation fields for asymptotically Euclidean manifolds, introduced by F.G. Friedlander, we define radiation fields for asymptotically hyperbolic manifolds. We use them to give a translation representation of the wave group and to obtain the scattering matrix for such manifolds. Furthermore, we prove a support theorem for the radiation fields which generalizes to this setting the well known support theorem of Helgason and Lax & Phillips for the horocyclic Radon transform. This is used to show that the manifold and the metric, up to invariants, are determined by the scattering matrix at all energies.

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تاریخ انتشار 2003