April 14, 2024Open Access

Polynomial Fourier Decay For Patterson-Sullivan Measures

Key Points

Key points are not available for this paper at this time.

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 L²-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.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Osama Khalil (Sun,) studied this question.

synapsesocial.com/papers/68e6f4b7b6db64358766ee44 https://doi.org/https://doi.org/10.48550/arxiv.2404.09424

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Spectral gaps and Fourier decay for self-conformal measures in the plane2024
2Spectral gaps and Fourier decay for self-conformal measures on the plane2026 · 1 citations
3Sharp Fourier decay estimates for measures supported on the well-approximable numbers2024
4Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set2026
5Convexity, Fourier transforms, and lattice point discrepancy2024

Bookmark

View Full Paper