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# Higher Order Scattering on Asymptotically Euclidean Manifolds

Published:2000-10-01
Printed: Oct 2000
• T. J. Christiansen
• M. S. Joshi
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## 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 $\pi$ 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.
 Keywords: scattering theory, conormal, Lagrangian
 MSC Classifications: 58G15 - unknown classification 58G15

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