Convergence of spherical averages for actions of free groups
| dc.creator | Bufetov, Alexander I. | |
| dc.date | 2005-07-12 | |
| dc.date.accessioned | 2026-07-07T05:21:37Z | |
| dc.date.available | 2026-07-07T05:21:37Z | |
| dc.description | 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. | |
| dc.description | 16 pages, published version | |
| dc.identifier | https://arxiv.org/abs/math/0507243 | |
| dc.identifier | http://arxiv.org/abs/math/0507243 | |
| dc.identifier | Annals of Math. (2), Vol. 155 (2002), no. 3, 929--944 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75758 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A30; 47A35 | |
| dc.title | Convergence of spherical averages for actions of free groups | |
| dc.type | text |