Decay of Fourier coefficients for Furstenberg measures

Dinh, Tien-Cuong; Kaufmann, Lucas; Wu, Hao

doi:10.1090/tran/8882

Decay of Fourier coefficients for Furstenberg measures
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by Tien-Cuong Dinh, Lucas Kaufmann and Hao Wu;

Trans. Amer. Math. Soc. 376 (2023), 6873-6926

DOI: https://doi.org/10.1090/tran/8882

Published electronically: July 20, 2023

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Abstract:

Let $\nu$ be the Furstenberg measure associated with a non-elementary probability measure $\mu$ on $SL_2(\mathbb {R})$. 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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