The spectrum of Kleinian manifolds

We obtain the Plancherel theorem for L-2(Gamma\G), where G is a classical s imple Lie group of real rank one and Gamma subset of G is convex-cocompact discrete subgroup, and deduce its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian manifolds. As the main tool, we develop a geometric version of scattering theory which, in p articular, contains the meromorphic continuation of the Eisenstein series f or this situation. The central role played by invariant distribution sectio ns supported on the limit set is emphasized. (C) 2000 Academic Press.