Higher Order Scattering on Asymptotically Euclidean Manifolds
Printed: Oct 2000
T. J. Christiansen
M. S. Joshi
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.
scattering theory, conormal, Lagrangian
58G15 - unknown classification 58G15