English

Finite Riesz products and Ornstein non-inequalities on quantum tori

Operator Algebras 2026-04-23 v1 Functional Analysis

Abstract

We demonstrate a construction of products on the quantum torus Tθ2\mathbb{T}_\theta^2 that generalises the usual construction of finite Riesz products on the commutative torus T2\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.

Keywords

Cite

@article{arxiv.2604.20774,
  title  = {Finite Riesz products and Ornstein non-inequalities on quantum tori},
  author = {Christos P. Tantalakis and Michał Wojciechowski},
  journal= {arXiv preprint arXiv:2604.20774},
  year   = {2026}
}