On group actions with simple Lebesgue spectrum

TL;DR

This paper introduces a method to construct measure-preserving actions of the Euclidean group with Lebesgue spectrum of multiplicity one, advancing the understanding of spectral properties in ergodic theory.

Contribution

It provides a novel construction of group actions exhibiting simple Lebesgue spectrum, which was previously unresolved.

Findings

Successfully constructs actions with Lebesgue spectrum of multiplicity one.

Advances the theory of spectral types in ergodic group actions.

Offers new tools for analyzing spectral properties of measure-preserving systems.

Abstract

In this paper we propose a construction of measure preserving actions of the group $R^d$ with Lebesgue spectrum of multiplicity one.