Semiclassical limits of distorted plane waves in chaotic scattering without a pressure condition

In this paper, we study the semi-classical 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 $L_{loc}^2$ independently of $h$, that they admit a unique semiclassical measure, and we prove bounds on their $L_{loc}^p$ norms.