Limiting absorption principle for long-range perturbations of pseudo-differential operators

The main purpose of this paper is to prove the limiting absorption principle and the absence of singularly continuous spectrum for hamiltonians of the form H=h(P)+V(Q, P), where Q (resp. P) is the position (resp. momentum) operator. We are especially interested in the case when the kinetic energy h(k) does not tend to infinity when the momentum k tends to infinity; moreover, we do not assume that the velocity ∇h(k) triple bond h'(k) is dominated by the kinetic energy. (orig.)