English

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.

Keywords

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

R2 v1 2026-06-22T21:59:51.867Z