Open Access
June 2019 A Dirichlet approximation theorem for group actions
Clayton Petsche, Jeffrey D. Vaaler
Funct. Approx. Comment. Math. 60(2): 263-275 (June 2019). DOI: 10.7169/facm/1755


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. "A Dirichlet approximation theorem for group actions." Funct. Approx. Comment. Math. 60 (2) 263 - 275, June 2019.


Published: June 2019
First available in Project Euclid: 26 June 2018

zbMATH: 07068536
MathSciNet: MR3964265
Digital Object Identifier: 10.7169/facm/1755

Primary: 11J25
Secondary: 22F10 , ‎37B05‎

Keywords: continuous group actions , unitary group

Rights: Copyright © 2019 Adam Mickiewicz University

Vol.60 • No. 2 • June 2019
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