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Semiclassical limits of distorted plane waves in chaotic scattering without a pressure condition. (arXiv:1706.07691v1 [math.SP])

来源于:arXiv
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 $L^2_{loc}$ independently of $h$, that they admit a unique semiclassical measure, and we prove bounds on their $L^p_{loc}$ norms. 查看全文>>