MICROLOCAL PROPAGATION NEAR RADIAL POINTS AND SCATTERING FOR SYMBOLIC POTENTIALS OF ORDER ZERO

In this paper, the scattering and spectral theory of H = Δ_g +V is developed, where Δ_g is the Laplacian with respect to a scattering metric g on a compact manifold X with boundary and (Formula Presented) is real; this extends our earlier results in the two-dimensional case. Included in this class of operators are perturbations of the Laplacian on Euclidean space by potentials homogeneous of degree zero near infinity. Much of the particular structure of geometric scattering theory can be traced to the occurrence of radial points for the underlying classical system. In this case the radial points correspond precisely to critical points of the restriction, V₀, of V to ∂X and under the additional assumption that V0 is Morse a functional parameterization of the generalized eigenfunctions is obtained.