Higher order scattering on asymptotically Euclidean Manifolds
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Spectral Theory
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.
Cite
@article{arxiv.math/0002148,
title = {Higher order scattering on asymptotically Euclidean Manifolds},
author = {T. J. Christiansen and M. S. Joshi},
journal= {arXiv preprint arXiv:math/0002148},
year = {2007}
}
Comments
To appear in the Canadian Journal of Mathematics; 26 pages