DECAY OF FOURIER COEFFICIENTS FOR FURSTENBERG MEASURES

Abstract

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