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arXiv · 2404.09424

Polynomial Fourier Decay For Patterson-Sullivan Measures

Osama Khalil
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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 $L^2$-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.

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Osama Khalil. 2024-04-15. Polynomial Fourier Decay For Patterson-Sullivan Measures. https://arxiv.org/abs/2404.09424

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