Generalized Riesz Products on the Bohr compactification of $\R$

TL;DR

This paper investigates singular generalized Riesz products on the Bohr compactification of A, using a Central Limit Theorem to analyze spectral types of rank one flows and exploring flat polynomials in this context.

Contribution

It introduces a new class of singular generalized Riesz products on the Bohr compactification of A and applies a Central Limit Theorem to study their spectral properties.

Findings

Identification of a large class of singular Riesz products.

Application of Kac's Central Limit Theorem in this setting.

Discussion on the problem of flat polynomials on the Bohr compactification.

Abstract

We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on $\R$. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of $\R$. Moreover, we discuss the problem of the flat polynomials in this setting.