Semiclassical Limits of Distorted Plane Waves in Chaotic Scattering Without a Pressure Condition

Abstract

Abstract In this paper, we study the semiclassical behavior of distorted plane waves, on manifolds that are Euclidean near infinity or hyperbolic near infinity, and of non-positive curvature. Assuming that there is a strip without resonances below the real axis, we show that distorted plane waves are bounded in $L^2_{loc}$ independently of $h$ and that they admit a unique semiclassical measure and we prove bounds on their $L^p_{loc}$ norms.