  In this paper we consider certain asymptotically Euclidean spaces, namely
compact manifolds with boundary X equipped with a scattering metric g, as
defined by Melrose. We then consider Hamiltonians H which are `short-range'
self-adjoint perturbations of the Laplacian of g. Melrose and Zworski have
given a detailed description of the associated scattering matrix and Poisson
operator as a Fourier integral operator and a (singular) Legendre distribution
respectively. In this paper we describe the kernel of the spectral projections
and the boundary value of the resolvent at the real axis. We define classes of
Legendre distributions on certain types of manifolds with corners, and show
that the kernels of the spectral projection and the resolvent are in these
classes. We also discuss some applications of these results.
