Grid method for divergence of averages

نویسندگان

چکیده

Abstract In this paper, we will introduce the ‘grid method’ to prove that extreme case of oscillation occurs for averages obtained by sampling a flow along sequence times form $\{n^\alpha : n\in {\mathbb {N}}\}$ , where $\alpha $ is positive non-integer rational number . Such behavior known as strong sweeping-out property By using same method, give an example general class sequences which satisfy property. This may be useful solve long-standing open problem: given irrational whether $(n^\alpha )$ bad pointwise ergodic theorem in $L^2$ or not. process proving result, also continuous version Conze principle.

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ژورنال

عنوان ژورنال: Ergodic Theory and Dynamical Systems

سال: 2023

ISSN: ['0143-3857', '1469-4417']

DOI: https://doi.org/10.1017/etds.2023.29