Decay of Fourier coefficients for Furstenberg measures

Let ν \nu be the Furstenberg measure associated with a non-elementary probability measure μ \mu on S L 2 ( R ) SL_2(\mathbb {R}) . We show that, when μ \mu has a finite second moment, the Fourier coefficients of ν \nu tend to zero at infinity. In other words, ν \nu is a Rajchman measure. This improv...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2023-10
Main Authors: Dinh, Tien-Cuong, Kaufmann, Lucas, Wu, Hao
Format: Article
Language:English
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Summary:Let ν \nu be the Furstenberg measure associated with a non-elementary probability measure μ \mu on S L 2 ( R ) SL_2(\mathbb {R}) . We show that, when μ \mu has a finite second moment, the Fourier coefficients of ν \nu tend to zero at infinity. In other words, ν \nu is a Rajchman measure. This improves a recent result of Jialun Li.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/8882