On the spectral type of some class of rank one flows

Abstract

It is shown that a certain class of Riesz product type measure on $\mathbb{R}$ is singular. This proves the singularity of the spectral types of some class of rank one flows. Our method is based on the extension of the Central Limit Theorem approach to the real line which gives a new extension of Salem-Zygmund Central Limit Theorem.

arXiv commentrevised version with 19 pages. Submitted for publication