Mixing rates for linear operators under infinitely divisible measures on Banach spaces

TL;DR

This paper establishes explicit mixing rates for linear operators on Banach spaces under infinitely divisible measures, extending Gaussian results to broader classes like stable and compound Poisson measures.

Contribution

It introduces a new framework for analyzing mixing rates using codifference functionals, generalizing previous Gaussian-based methods to a wider class of infinitely divisible measures.

Findings

Derived explicit mixing rates for weighted shifts under various infinitely divisible measures.

Extended Gaussian mixing results to stable and tempered stable measures.

Provided a characterization of mixing in terms of codifference functionals.

Abstract

We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference functionals and control measures, and extends previous results obtained in the Gaussian setting via the use of covariance operators. Explicit mixing rates are obtained for weighted shifts under compound Poisson, {\alpha}-stable, and tempered {\alpha}-stable measures.