2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69325We show that the resolvent of the Laplacian on asymptotically hyperbolic spaces extends meromorphically with finite rank poles to the complex plane if and only if the metric is `even' (in a sense). If it is not even, there exist some cases where the resolvent has an essential singularity in the non-physical sheet.23 pages, 2 figuresSpectral TheoryMathematical PhysicsAnalysis of PDEs58J50, 35P25text