We show a fractal uncertainty principle with exponent
,
, for Ahlfors–David
regular subsets of
of dimension
.
This is an improvement over the volume bound
, and
is
estimated explicitly in terms of the regularity constant of the set. The proof uses a
version of techniques originating in the works of Dolgopyat, Naud, and Stoyanov on
spectral radii of transfer operators. Here the group invariance of the set is replaced by
its fractal structure. As an application, we quantify the result of Naud on spectral
gaps for convex cocompact hyperbolic surfaces and obtain a new spectral gap for
open quantum baker maps.
We have not been able to recognize your IP address
18.207.133.27
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.