On the spectral type of some class of rank one flows

TL;DR

This paper demonstrates that a specific class of rank one flows have singular spectral measures by extending the Central Limit Theorem approach to the real line, providing new insights into spectral theory.

Contribution

It introduces a novel extension of the Salem-Zygmund Central Limit Theorem to analyze the spectral type of rank one flows, establishing their singularity.

Findings

Certain rank one flows have singular spectral measures

Extension of CLT to the real line is effective for spectral analysis

Provides new tools for spectral type classification in ergodic theory

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.