Fractal Uncertainty Principle with Explicit Exponent
Classical Analysis and ODEs
2018-06-06 v3 Analysis of PDEs
Spectral Theory
Abstract
We prove an explicit formula for the dependence of the exponent in the fractal uncertainty principle of Bourgain-Dyatlov on the dimension and on the regularity constant for the regular set. In particular, this implies an explicit essential spectral gap for convex co-compact hyperbolic surfaces when the Hausdorff dimension of the limit set is close to 1.
Cite
@article{arxiv.1710.00250,
title = {Fractal Uncertainty Principle with Explicit Exponent},
author = {Long Jin and Ruixiang Zhang},
journal= {arXiv preprint arXiv:1710.00250},
year = {2018}
}
Comments
23 pages, 2 figures, Errors corrected