# Decay of Fourier coefficients for Furstenberg measures

@inproceedings{Dinh2021DecayOF, title={Decay of Fourier coefficients for Furstenberg measures}, author={T. C. Dinh and Lucas Kaufmann and Hao Wu}, year={2021} }

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.

## One Citation

### Random walks on SL_2(C): spectral gap and limit theorems

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We obtain various new limit theorems for random walks on SL2(C) under low moment conditions. For non-elementary measures with a finite second moment we prove a Local Limit Theorem for the norm…

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