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Radiation fields, scattering and inverse scattering on asymptotically hyperbolic manifolds
, 2004
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Radiation fields for semilinear wave equations
 In preparation
, 2012
"... Abstract. We define the radiation fields of solutions to critical semilinear wave equations in R 3 and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the well known support theorem for the Radon transform to ..."
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Abstract. We define the radiation fields of solutions to critical semilinear wave equations in R 3 and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the well known support theorem for the Radon transform to this setting and can also be interpreted as a PaleyWiener theorem for the distorted nonlinear Fourier transform of radial functions. 1.
SCATTERING AND INVERSE SCATTERING ON ACH MANIFOLDS
, 2006
"... We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is a contact manifold with a pseudohermitian structure. Then ..."
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We study scattering and inverse scattering theories for asymptotically complex hyperbolic manifolds. We show the existence of the scattering operator as a meromorphic family of operators in the Heisenberg calculus on the boundary, which is a contact manifold with a pseudohermitian structure. Then we define radiation fields as in the real asymptotically hyperbolic case, and reconstruct the scattering operator from those fields. As an application we show that the manifold, including its topology and the metric, are determined up to invariants by the scattering matrix at all energies.