Limiting absorption principle for singularly perturbed operators

Given an operator H-1 for which a limiting absorption principle holds, we s tudy operators H-2 which are produced by perturbing H-1 in the sense that t he difference between some powers of the resolvents is compact. We show tha t (except for possibly a discrete set of eigenvalues) a limiting absorption principle holds for H-2. We apply this theory to study potential and domain perturbations of Feller operators. While our theory mostly reproduces known results in the case of potential perturbations, for domain perturbations we get results which appe ar to be new.