2005Colloquium MathematicumOpen access

Pointwise convergence of nonconventional averages

Idris Assani

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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

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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

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Available 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

Key concepts: Pointwise convergence, Pointwise, Mathematics, Convergence (economics), Combinatorics, Discrete mathematics, Mathematical analysis, Approx

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