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• W2912653235 abstract "Let $Gamma$ be a Zariski dense Kleinian Schottky subgroup of PSL2(C). Let $Lambda(Gamma)$ be its limit set, endowed with a Patterson-Sullivan measure $mu$ supported on $Lambda(Gamma)$. We show that the Fourier transform $widehat{mu}(xi)$ enjoys polynomial decay as $vert xi vert$ goes to infinity. This is a PSL2(C) version of the result of Bourgain-Dyatlov [8], and uses the decay of exponential sums based on Bourgain-Gamburd sum-product estimate on C. These bounds on exponential sums require a delicate non-concentration hypothesis which is proved using some representation theory and regularity estimates for stationary measures of certain random walks on linear groups." @default.
• W2912653235 created "2019-02-21" @default.
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• W2912653235 date "2019-02-04" @default.
• W2912653235 modified "2023-09-25" @default.
• W2912653235 title "Kleinian Schottky groups, Patterson-Sullivan measures and Fourier decay" @default.
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• W2912653235 doi "https://doi.org/10.48550/arxiv.1902.01103" @default.
• W2912653235 hasPublicationYear "2019" @default.
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