N-BODY HAMILTONIANS WITH HARD-CORE INTERACTIONS

We study N-body hamiltonians with short and long range potentials whic h are infinite on compact sets of non-zero measure. We show that the g enerator of the dilation group is locally conjugated to them away from the threshold energies. The notion of conjugacy has to be interpreted in a very weak sense, but this is enough to deduce an optimal form of the limiting absorption principle, and so absence of singular continu ous spectrum and local decay. One of the main technical steps of our a pproach requires a maximal regularity result for the Dirichlet Laplaci an in an open set with irregular boundary. We prove it for a large cla ss of non-smooth domains.