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Mathematics > Dynamical Systems
Title: Polynomial Fourier Decay For Patterson-Sullivan Measures
(Submitted on 15 Apr 2024)
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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