Bufetov, Alexander I.; Khristoforov, Mikhail; Klimenko, Alexey Cesàro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups. (English) Zbl 1267.22003 Int. Math. Res. Not. 2012, No. 21, 4797-4829 (2012). The authors prove, in their main theorem (Theorem 1), that the sequence of Cesaro averages of the spherical averages, of a Markov semigroup \(\Gamma\) with respect to a finite generating set, converges. The result in Theorem 1 provides the mean convergence of the sequence of Cesaro averages for functions in \(L^p\) and pointwise convergence for functions in \(L^{\infty}\). The Markov semigroup \(\Gamma\) is assumed to act by measure-preserving transformations on a probability space. Therefore, the result in Theorem 1 will apply to all measure-preserving actions of word hyperbolic groups. Reviewer: Ioan Bucataru (Iaşi) Cited in 6 Documents MSC: 22D40 Ergodic theory on groups 28D05 Measure-preserving transformations Keywords:Marko semigroup; Cesaro convergence; spherical averages PDF BibTeX XML Cite \textit{A. I. Bufetov} et al., Int. Math. Res. Not. 2012, No. 21, 4797--4829 (2012; Zbl 1267.22003) Full Text: DOI arXiv OpenURL