Dolgopyat’s method and the fractal uncertainty principle
Name
1702.03619.pdf
Description
Accepted version
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572.26 KB
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Author(s)
Dyatlov, Semyon
Jin, Long
Date Issued
May 2018
Journal
Analysis & PDE
Publisher
Mathematical Sciences Publishers
Citation
Dyatlov, Semyon and Long Jin. "Dolgopyat's method and the fractal uncertainty principle." Analysis & PDE 11, 6 (May 2018): 1457-1485 © 2018 Mathematical Sciences Publishers
Version
Author's final manuscript
Abstract
We show a fractal uncertainty principle with exponent 1/2-δ+ε, ε > 0, for Ahlfors-David regular subsets of ℝ of dimension δ ∈ (0,1). This is an improvement over the volume bound 1/2-δ, and ε 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.2140/APDE.2018.11.1457
