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arXiv · 2404.07907

On orthogonality to uniquely ergodic systems

Martyna Górska·Mariusz Lemańczyk·Thierry de la Rue
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Abstract

We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some variations of Boshernitzan's problem involving characteristic classes are considered. As an application, we characterize sequences orthogonal to all uniquely ergodic systems whose (unique) invariant measure yields a discrete spectrum automorphism as those satisfying an averaged Chowla property.

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Martyna Górska, Mariusz Lemańczyk, Thierry de la Rue. 2024-04-11. On orthogonality to uniquely ergodic systems. https://arxiv.org/abs/2404.07907

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