Fractal Uncertainty Principle with Explicit Exponent

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.

23 pages, 2 figures, Errors corrected

References in corpus (3)

• Spectral gaps without the pressure condition
• Resonances for open quantum maps and a fractal uncertainty principle
• A higher dimensional Bourgain-Dyatlov fractal uncertainty principle

Cited by in corpus (2)

• An introduction to fractal uncertainty principle
• A higher dimensional Bourgain-Dyatlov fractal uncertainty principle