Higher order scattering on asymptotically Euclidean Manifolds

Details Higher order scattering on asymptotically Euclidean Manifolds Higher order scattering on asymptotically Euclidean Manifolds

2000-02-17

arxiv.org/abs/math/0002148v1

Mathematics

Analysis of PDEs

To appear in the Canadian Journal of Mathematics; 26 pages

Scientific paper

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 \pi on the boundary. Furthermore, it is shown that on \Real^n the asymptotics of certain short-range perturbations of \Delta^k can be recovered from the scattering matrix at a finite number of energies.

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