Lebesgue Component in Spectrum for Tensor Product of Generic Multiplies

TL;DR

This paper investigates the spectral properties of tensor products of certain measure-preserving transformations, demonstrating the presence of Lebesgue components in their spectra through examples involving Gaussian and Poisson systems.

Contribution

It introduces new examples of measure-preserving systems with Lebesgue spectral components in their tensor products, expanding understanding of spectral interactions.

Findings

Lebesgue components in tensor product spectra of specific transformations

Examples involving Gaussian and Poisson suspensions

Spectral interactions in rigid systems

Abstract

Generic (rigid) measure-preserving transformations with Lebesgue component in spectrum of their tensor product, two rigid Gaussian systems and two rigid Poisson suspensions with similar spectral interactions are presented.