Symbolic Functional Calculus and N-Body Resolvent Estimates

We construct a functional calculus for symbolic functions of “scattering pseudodifferential operators” on manifolds with boundary. This is applied to obtain mapping results on the scattering wavefront set of the B operator used by Gérard et al. (1994, “Commutator Algebra and Resolvent Estimates,” Advanced Studies in Pure Mathematics, Vol. 23, Math. Soc. Japan, Tokyo) to obtain N-body resolvent estimates. As an application, we construct the plane waves for an N-body, short range Schrödinger operator and obtain a scattering wavefront set estimate.