Polynomial Fourier Decay For Patterson-Sullivan Measures

Autor:	Khalil, Osama
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
Popis:	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. Comment: This article has now been subsumed by arXiv:2407.16699. arXiv admin note: substantial text overlap with arXiv:2305.00527
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.09424 Zobrazit plný text záznamu View this record from Arxiv