Decay of Fourier coefficients for Furstenberg measures

2021/08/13 by Dinh, Tien-Cuong, Kaufmann, Lucas, Wu, Hao · 1 citation
#37C30 #42A16 #60B15 #60B20 #60K15 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2108.06006

Abstract

Let ν be the Furstenberg measure associated with a non-elementary probability measure μ on SL₂(R). We show that, when μ has a finite second moment, the Fourier coefficients of ν tend to zero at infinity. In other words, ν is a Rajchman measure. This improves a recent result of Jialun Li.

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