Semiclassical resolvent estimates for N-body Schrödinger operators

Abstract

In this paper we prove for a generalized N-body Schrödinger operator that the non-trapping condition on the classical hamiltonian and all classical subhamiltonians is both necessary and sufficient for obtaining good semiclassical bounds on the boundary values of the resolvent and their energy derivatives. We accomplish this by generalizing Gérard's geometrical construction of an escape function for three-body problems to N-body problems.