Averages along cubes for not necessarily commuting measure preserving transformations

Idris Assani

Averages along cubes for not necessarily commuting measure preserving transformations

Dynamical Systems 2016-09-07 v1

Authors: Idris Assani

Abstract

We study the pointwise convergence of some weighted averages linked to averages along cubes. We show that if $(X,\mathcal{B},\mu, T_i)$ are not necessarily commuting measure preserving systems on the same finite measure space and if $f_i,$ $1\leq i\leq 6$ are bounded functions then the averages $\frac{1}{N^3}\sum_{n, m, p=1}^N f_1(T_1^nx) f_2(T_2^mx) f_3(T_3^px) f_4(T_4^{n+m}x) f_5(T_5^{n+p}x) f_6(T_6^{m+p}x)$ converge almost everywhere.

Keywords

invariant measures interval exchange maps measure theory

Cite

@article{arxiv.math/0511062,
  title  = {Averages along cubes for not necessarily commuting measure preserving transformations},
  author = {Idris Assani},
  journal= {arXiv preprint arXiv:math/0511062},
  year   = {2016}
}

Comments

28 pages

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