A Poisson Formula for the Wave Propagator on Schwarzschild-de Sitter Backgrounds

Abstract: This paper proposes a Poisson formula for the wave propagator of the Schwarzschild--de Sitter (SdS) metric. That is done by proving a Poisson formula relating wave propagators and scattering resonances for a class of non-compactly supported potentials on the real line. That class includes the Regge--Wheeler potentials obtained from separation of variables for SdS. The novelty lies in allowing non-compact supports -- all exact Poisson formulae of Lax--Phillips, Melrose, and other authors required compactness of the support of the perturbation.