2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152166A Kleinian manifold Y is a quotient of a rank-one symmetric space of non-compact type by a convex-cocompact discrete group of isometries. We describe the spectral decomposition of the space of square integrable sections of locally homogeneous bundles on Y with respect to locally invariant differential operators. In the course of the proof we obtain meromorphic continuations of Eisenstein series and scattering matrices.64 pages, LATEXDifferential Geometrytext