Abstract
This paper deals with the spectrum of the perturbed Laplace-Beltrami operator acting on automorphic functions in n-dimensional real hyperbolic space. The discrete subgroup is assumed to have the finite geometric property but is otherwise not restricted. The approach uses the non-Euclidean wave equation and relies on the translation representation for the unperturbed system which was developed by Lax and Phillips. It is shown for short-range perturbations that the wave operators exist and are complete.
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