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- W2952314946 abstract "Convergence of non-uniform spherical averages is obtained for measure-preserving actions of free groups. This result generalizes theorems of Grigorichuk, Nevo and Stein [in particular, a simpler proof of the Nevo-Stein theorem about uniform spherical averages is obtained.] The proof uses the Markov operator approach, first proposed by R.I. Grigorchuk. To a measure-preserving action of a free group and a matrix of weights, a Markov operator is assigned in such a way that convergence of spherical averages with corresponding weights is equivalent to convergence of powers of the Markov operator. That last is obtained using Rota's Alternierende Verfahren; the 0-2 law for Markov operators in the form of Kaimanovich; and a suitable maximal inequality." @default.
- W2952314946 created "2019-06-27" @default.
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- W2952314946 date "2005-07-12" @default.
- W2952314946 modified "2023-09-27" @default.
- W2952314946 title "Convergence of spherical averages for actions of free groups" @default.
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