Polynomial Fourier Decay For Patterson-Sullivan Measures

Fuente: arXiv
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Autore principale: Khalil, Osama
Natura: Preprint
Pubblicazione: 2024
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author Khalil, Osama
author_facet Khalil, Osama
contents We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infinity. The proof is based on the $L^2$-flattening theorem obtained in prior work of the author, combined with a method based on dynamical self-similarity for ruling out the sparse set of potential frequencies where the Fourier transform can be large.
format Preprint
id arxiv_https___arxiv_org_abs_2404_09424
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Polynomial Fourier Decay For Patterson-Sullivan Measures
Khalil, Osama
Dynamical Systems
Classical Analysis and ODEs
Spectral Theory
We show that the Fourier transform of Patterson-Sullivan measures associated to convex cocompact groups of isometries of real hyperbolic space decays polynomially quickly at infinity. The proof is based on the $L^2$-flattening theorem obtained in prior work of the author, combined with a method based on dynamical self-similarity for ruling out the sparse set of potential frequencies where the Fourier transform can be large.
title Polynomial Fourier Decay For Patterson-Sullivan Measures
topic Dynamical Systems
Classical Analysis and ODEs
Spectral Theory
url https://arxiv.org/abs/2404.09424