Radiation Fields, Scattering and Inverse Scattering on Asymptotically Hyperbolic Manifolds

Details Radiation Fields, Scattering and Inverse Scattering on Asymptotically Hyperbolic Manifolds Radiation Fields, Scattering and Inverse Scattering on Asymptotically Hyperbolic Manifolds

2003-12-04

arxiv.org/abs/math/0312108v2

Mathematics

Analysis of PDEs

47 pages, 7 figures

Scientific paper

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 and 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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