Spectral decomposition of pseudo-cuspforms, and meromorphic continuation of Eisenstein series, on Q-rank one arithmetic quotients

Abstract

In this paper, we extend Lax-Phillips’ discreteness of pseudo-cuspforms, in the style of Colin de Verdiere’s use of the Friedrichs self-adjoint extension of a restriction of the Laplace-Beltrami operator, as opposed to the use of semigroup methods. We use this to prove meromorphic continuation of Eisenstein series in the Q-rank one case, again following Colin de Verdiere, as opposed to the semigroup-oriented viewpoint of Lax-Phillips and W. Mueller.