Higher Order Scattering on Asymptotically Euclidean Manifolds

Abstract

AbstractWe 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 π on the boundary. Furthermore, it is shown that on n the asymptotics of certain short-range perturbations of Δk can be recovered from the scattering matrix at a finite number of energies.