Decay of Fourier coefficients for Furstenberg measures
Abstract
Let $\nu$ be the Furstenberg measure associated with a nonelementary 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.06006
 Bibcode:
 2021arXiv210806006D
 Keywords:

 Mathematics  Probability;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Dynamical Systems;
 60B15;
 60B20;
 60K15;
 42A16;
 37C30
 EPrint:
 50 pages, v1>