Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups

Details Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups

2011-01-28

arxiv.org/abs/1101.5459v1

Mathematics

Dynamical Systems

32 pages

Scientific paper

Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\le p<\infty$, and pointwise convergence for functions in $L^\infty$. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.

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