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Higher Order Scattering on Asymptotically Euclidean Manifolds

Published online by Cambridge University Press:  20 November 2018

T. J. Christiansen  and
M. S. Joshi
T. J. Christiansen
Affiliation:
Department of Mathematics, University of Missouri, Columbia, Missouri 65211, USA email: tjc@math.missouri.edu
M. S. Joshi
Affiliation:
Darwin College, Cambridge CB3 9EU, UK
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Abstract

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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 ${{\mathbb{R}}^{n}}$ the asymptotics of certain short-range perturbations of ${{\Delta }^{k}}$ can be recovered from the scattering matrix at a finite number of energies.

Keywords

58G15scattering theoryconormalLagrangian

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 5 , 01 October 2000 , pp. 897 - 919
Copyright
Copyright © Canadian Mathematical Society 2000

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