Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations

Details Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations

2009-06-17

arxiv.org/abs/0906.3266v1

Mathematics

Dynamical Systems

Scientific paper

Let $(X,\mathcal{B},\mu)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\neq (0,...,0)$, then the averages $\frac{1}{|\Phi_N|}\sum_{u\in\Phi_N}\prod_{i=1}^r T_1^{p_{i1}(u)}... T_l^{p_{il}(u)}f_i$ converge in $L^2(\mu)$ for all polynomials $p_{ij}\colon \mathbb{Z}^d\to\mathbb{Z}$, all $f_i\in L^{\infty}(\mu)$, and all F{\o}lner sequences $\{\Phi_N\}_{N=1}^{\infty}$ in $\mathbb{Z}^d$.

Affiliated with

Also associated with

No associations

Rating

Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence of Polynomial Ergodic Averages of Several Variables for some Commuting Transformations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-223857