A simple proof of Bourgain's theorem on the singularity of the spectrum of Ornstein's maps

TL;DR

This paper provides a straightforward proof of Bourgain's theorem, establishing the singularity of the spectrum for Ornstein's maps, which are important in ergodic theory.

Contribution

The authors present a simplified proof of Bourgain's theorem, making the result more accessible and easier to understand.

Findings

Proof confirms the spectrum of Ornstein's maps is singular.

Simplifies the understanding of Bourgain's theorem.

Enhances accessibility of spectral analysis in ergodic theory.

Abstract

We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.