An introduction to fractal uncertainty principle
Classical Analysis and ODEs
2019-08-20 v2 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1903.02599,
title = {An introduction to fractal uncertainty principle},
author = {Semyon Dyatlov},
journal= {arXiv preprint arXiv:1903.02599},
year = {2019}
}
Comments
45+eps pages, 16 figures. To appear in Journal of Mathematical Physics