Pointwise convergence of nonconventional averages
Volume 102 / 2005
Colloquium Mathematicum 102 (2005), 245-262
MSC: 37A05, 37A30, 47A35.
DOI: 10.4064/cm102-2-6
Abstract
We answer a question of H. Furstenberg on the pointwise convergence of the averages $$\frac{1}{N}\sum_{n=1}^N U^{n}(f \cdot R^{n}(g)),$$ where $U$ and $R$ are positive operators. We also study the pointwise convergence of the averages $$\frac{1}{N}\sum_{n=1}^N f(S^nx)g(R^nx)$$ when $T$ and $S$ are measure preserving transformations.
