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arXiv · 2108.06006

Decay of Fourier coefficients for Furstenberg measures

Tien-Cuong Dinh·Lucas Kaufmann·Hao Wu
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Abstract

Let $\nu$ be the Furstenberg measure associated with a non-elementary probability measure $\mu$ on SL_2(R). We show that, when $\mu$ has a finite second moment, the Fourier coefficients of $\nu$ tend to zero at infinity. In other words, $\nu$ is a Rajchman measure. This improves a recent result of Jialun Li.

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Tien-Cuong Dinh, Lucas Kaufmann, Hao Wu. 2021-08-13. Decay of Fourier coefficients for Furstenberg measures. https://arxiv.org/abs/2108.06006

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