Asymptotic Behavior of Generalized Eigenfunctions inN-Body Scattering

In this paper an asymptotic expansion is proved for locally (at infinity) outgoing functions on asymptotically Euclidian spaces. This is applied toN-body scattering where the two-body interactions are one-step polyhomogeneous symbols of order −1 or −2 (hence long-range and short-range, respectively). The asymptotic behavior of theN-body resolvent applied to Schwartz functions is thereby deduced away from the singular set, where some of the potentials do not decay at infinity.