Higher order scattering on asymptotically Euclidean Manifolds
T. J. Christiansen, M. S. Joshi
Abstract
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time πon the boundary. Furthermore, it is shown that on n the asymptotics of certain short-range perturbations of Δk can be recovered from the scattering matrix at a finite number of energies.
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