Pointwise convergence of nonconventional averages

I. Assani¹

¹ Department of Mathematics, UNC Chapel Hill, NC 27599, U.S.A.

Colloquium Mathematicum, Tome 102 (2005) no. 2, pp. 245-262.

Résumé

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.

Détail

DOI : 10.4064/cm102-2-6

Keywords: answer question furstenberg pointwise convergence averages frac sum cdot where positive operators study pointwise convergence averages frac sum measure preserving transformations