An introduction to fractal uncertainty principle
arXiv:1903.02599 · doi:10.1063/1.5094903
Abstract
Fractal uncertainty principle states that no function can be localized in both position and frequency near a fractal set. This article provides a review of recent developments on the fractal uncertainty principle and of their applications to quantum chaos, including lower bounds on mass of eigenfunctions on negatively curved surfaces and spectral gaps on convex co-compact hyperbolic surfaces.
45+eps pages, 16 figures. To appear in Journal of Mathematical Physics