Duke Mathematical Journal
- Duke Math. J.
- Volume 129, Number 3 (2005), 407-480.
Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds
We define the forward and backward radiation fields on an asymptotically hyperbolic manifold and show that they give unitary translation representations of the wave group and as such can be used to define a scattering matrix. We show that this scattering matrix is equivalent to the one defined by stationary methods. Furthermore, we prove a support theorem for the radiation fields which generalizes to this setting well-known results of Helgason  and Lax and Phillips  for the horocyclic Radon transform. As an application, we use the boundary control method of Belishev  to show that an asymptotically hyperbolic manifold is determined up to invariants by the scattering matrix at all energies.
Duke Math. J., Volume 129, Number 3 (2005), 407-480.
First available in Project Euclid: 19 October 2005
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Sá Barreto, Antônio. Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds. Duke Math. J. 129 (2005), no. 3, 407--480. doi:10.1215/S0012-7094-05-12931-3. https://projecteuclid.org/euclid.dmj/1129729971