论文标题
维度2中障碍物散射的光谱差距2
Spectral gap for obstacle scattering in dimension 2
论文作者
论文摘要
在本文中，我们研究了通过几个严格凸出障碍物散射的问题，并具有光滑的边界并满足非日食条件。我们仅在维度2中显示，存在光谱差距，用于在障碍物之外的拉普拉斯操作员的meromorphic延续。该结果的证明依赖于[Arxiv：1105.3128]中实现的开放双曲线量子图的减少。实际上，我们获得了此类对象的光谱差距，该差距也具有潜在散射中的应用。本文的第二个主要要素是分形的不确定性原理。我们适应了[Arxiv：1906.08923]的技术，以在我们的背景下应用这种分形不确定性原理。
In this paper, we study the problem of scattering by several strictly convex obstacles, with smooth boundary and satisfying a non eclipse condition. We show, in dimension 2 only, the existence of a spectral gap for the meromorphic continuation of the Laplace operator outside the obstacles. The proof of this result relies on a reduction to an open hyperbolic quantum map, achieved in [arXiv:1105.3128]. In fact, we obtain a spectral gap for this type of objects, which also has applications in potential scattering. The second main ingredient of this article is a fractal uncertainty principle. We adapt the techniques of [arXiv:1906.08923] to apply this fractal uncertainty principle in our context.
