Structure of the resolvent for three-body potentials (Q1376031)

The author investigates the three-body scattering matrix of Schrödinger operators. His main result is a proof of Melrose's conjecture on the three-cluster to three-cluster part of the scattering matrix, stating that it can be written as a sum of Fourier integral operators associated to a certain ``broken'' geodesic flow. The structure of the paper is as follows: analysis of the two-body resolvent, construction of the approximate eigenfunctions of the Schrödinger operator, construction of the three-body resolvent, facts on the Poisson operator, analysis of the scattering matrix, and finally, asymptotic behavior of the resolvent.