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arXiv · 2604.20774

Finite Riesz products and Ornstein non-inequalities on quantum tori

Christos P. Tantalakis·Michał Wojciechowski
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Abstract

We demonstrate a construction of products on the quantum torus $\mathbb{T}_\theta^2$ that generalises the usual construction of finite Riesz products on the commutative torus $\mathbb{T}^2$. We explain why the former constitutes a natural analogue of the latter in the non-commutative setting and, based on this construction, as well as on previous results by K. Kazaniecki and the second author, we prove a non-commutative version of an Ornstein non-inequality.

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Christos P. Tantalakis, Michał Wojciechowski. 2026-04-22. Finite Riesz products and Ornstein non-inequalities on quantum tori. https://arxiv.org/abs/2604.20774

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