In this paper an asymptotic expansion is proved for locally (at infinity) outgoing functions on asymptotically Euclidian spaces. This is applied to N-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 the N-body resolvent applied to Schwartz functions is thereby deduced away from the singular set. where some of the potentials do not decay at infinity. (C) 1997 Academic Press. [References: 10]
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