Inducing countable Lebesgue spectrum

TL;DR

This paper proves that any ergodic dynamical system can be transformed into a system with a pure Lebesgue spectrum of infinite multiplicity, revealing a fundamental spectral property.

Contribution

It introduces a method to induce systems with pure Lebesgue spectrum of infinite multiplicity from any ergodic dynamical system.

Findings

Every ergodic system induces a system with Lebesgue spectrum

The induced spectrum has infinite multiplicity

Spectral properties are preserved under induction

Abstract

We show that every ergodic dynamical system induces a system with pure Lebesgue spectrum of infinite multiplicity.