Asymptotic expansion in measure and strong ergodicity

Autor: Li, Kang, Vigolo, Federico, Zhang, Jiawen

In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on the classical notion of strong ergodicity. Moreover, we obtain structure

Externí odkaz: http://arxiv.org/abs/2005.05697

Ergodic Abelian actions with homogeneous spectrum

Autor: Danilenko, Alexandre I., Solomko, Anton V.

It is shown that for each $N>0$ and for a wide class of Abelian non-compact locally compact second countable groups $G$ including all infinite countable discrete ones and $\Bbb R^{d_1}\times\Bbb Z^{d_2}$ with $d_1,d_2\ge 0$, there exists a weakly mix

Externí odkaz: http://arxiv.org/abs/1001.2259

Cesàro Convergence of Spherical Averages for Measure-Preserving Actions of Markov Semigroups and Groups

Autor: Mikhail Khristoforov, Alexey Klimenko, Alexander I. Bufetov

Publikováno v: International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2012
International Mathematics Research Notices, 2012

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
Comment: 32 pages

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c10558d1515bf70a339dd68abb89533
https://doi.org/10.1093/imrn/rnr181