Resolvent bounds for repulsive potentials

Abstract

We prove limiting absorption resolvent bounds for the semiclassical Schrödinger operator with a repulsive potential in dimension $n\ge 3$, which may have a singularity at the origin. As an application, we obtain time decay for the weighted energy of the solution to the associated wave equation with a short range repulsive potential and compactly supported initial data.

27 pages