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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectral types of uniform distribution


Author: Geon H. Choe
Journal: Proc. Amer. Math. Soc. 120 (1994), 715-722
MSC: Primary 47A35; Secondary 11K06, 28D05
MathSciNet review: 1169880
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Abstract: We investigate the spectral types of unitary operator $ U$ on $ {L^2}(\mathbb{T})$ defined by $ (Uf)(x) = A(x)f(x + \theta ),\vert A(x)\vert = 1$ a.e., where $ \mathbb{T}$ is the unit circle identified with the half open interval $ [0,1)$ and $ \theta $ is irrational. It is shown that Veech's result on the Kronecker-Weyl theorem modulo $ 2$ is closely related to the spectral type of $ U$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1169880-6
PII: S 0002-9939(1994)1169880-6
Keywords: Maximal spectral type, uniform distribution modulo $ 1$, coboundary
Article copyright: © Copyright 1994 American Mathematical Society