Polynomial Fourier Decay For Patterson-Sullivan Measures
Dynamical Systems
2024-07-29 v2 Classical Analysis and ODEs
Spectral Theory
Abstract
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 -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.
Cite
@article{arxiv.2404.09424,
title = {Polynomial Fourier Decay For Patterson-Sullivan Measures},
author = {Osama Khalil},
journal= {arXiv preprint arXiv:2404.09424},
year = {2024}
}
Comments
This article has now been subsumed by arXiv:2407.16699. arXiv admin note: substantial text overlap with arXiv:2305.00527