Quantitative Fourier decay for Patterson-Sullivan measures of dimension larger than 1/2

2026/07/20 by Félix Lequen, Tuomas Sahlsten · 1 citation
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Abstract

We give an elementary proof of power Fourier decay for Patterson-Sullivan measures associated to convex co-compact Schottky groups of dimension δ>\frac12, obtaining the explicit decay exponent (δ(2δ- 1))/((2δ+ 1)(3 - δ)). The proof replaces the technical machinery used in previous works, such as sum-product estimates, renewal theory, Dolgopyat methods, and L² flattening, by elementary oscillatory integral estimates, hyperbolic geometry, and a duality argument based on the transpose Schottky group.

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