Spectral and scattering theory for the Laplacian on asymptotically Euclidian spaces

There are many approaches to conventional Euclidian scattering theory. In this exposition an essentially microlocal view is adopted. Apart from its intrinsic interest this is intended as preparation for later generalization, to more complicated geometric settings. In fact, the treatment given here extends beyond the usual confines of scattering theory in that the spectral and scattering theory, at least the elementary part, is covered for the Laplacian associated to a ‘scattering metric’ on any compact manifold with boundary. By a scattering metric on a compact manifold with boundary,X, we shall mean a Riemann metric on the interior of X which can be brought to the form