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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Eigenvalues of some distal functions


Author: Jiro Egawa
Journal: Proc. Amer. Math. Soc. 126 (1998), 273-278
MSC (1991): Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-98-04488-8
MathSciNet review: 1458868
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Abstract: In this paper we construct distal functions of another type discussed by Salehi (1991). Let $a(t)$ be an almost periodic function with the mean value 0, which has unbounded integral, and $\Phi$ a continuous periodic function with the prime period 1. If $\Phi$ satisfies some additional condition, then $f(t)=\Phi(\int^t_0a(s)\,ds)$ is a distal function, which is not almost periodic, and the set of eigenvalues of $f$ is the module of $a$.


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Additional Information

Jiro Egawa
Affiliation: Division of Mathematics and Informatics, Faculty of Human Development, Kobe University, Turukabuto 3-11, Nada, Kobe 657, Japan
Email: egawa@main.h.kobe-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-98-04488-8
Keywords: Equicontinuous, distal, minimal flow, almost periodic function, eigenvalues
Received by editor(s): November 28, 1995
Dedicated: Dedicated to Professor Junji Kato on his sixtieth birthday
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society