Mixing rates for linear operators under infinitely divisible measures on Banach spaces
Studia Mathematica
MSC: Primary 37A25; Secondary 47A35, 60G57, 60E07, 60G52, 37A05
DOI: 10.4064/sm250103-14-11
Published online: 18 May 2026
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.
