Lower Bounds on the Number of Scattering Poles, II

We obtain lower bounds on the number of scattering poles for a class of abstract compactly supported perturbations of the Laplacian in Rn, n odd. They are applied to estimate the number of resonances for obstacle scattering and for hypoelliptic compactly supported perturbations of the Laplacian. The proof involves a development of Lax-Phillips theory in a generalized setting, a Poisson formula for scattering poles, and some simple Tauberian arguments.