The spectrum of Kleininan manifolds

Abstract

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian manifolds. We develop a geometric version of scattering theory. The paper is an update of dg-ga/9609011, which is completely rewritten from the point of view of representation theory. In particular, we are now able to show the meromorphy of Eisenstein series for all parameters.