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arXiv · 1705.00562

A Dirichlet approximation theorem for group actions

Clayton Petsche·Jeffrey D. Vaaler
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Abstract

If $G$ is a compact group acting continuously on a compact metric space $(X, m)$, we prove two results that generalize Dirichlet's classical theorem on Diophantine approximation. If $G$ is a noncommutative compact group of isometries, we obtain a noncommutative form of Dirichlet's theorem. We apply our general result to the special case of the unitary group $U(N)$ acting on the complex unit sphere, and obtain a noncommutative result in this setting.

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Clayton Petsche, Jeffrey D. Vaaler. 2017-05-01. A Dirichlet approximation theorem for group actions. https://arxiv.org/abs/1705.00562

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