Eigenvalues of some distal functions
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- by Jirō Egawa PDF
- Proc. Amer. Math. Soc. 126 (1998), 273-278 Request permission
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 $a$.References
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Additional Information
- Jirō 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
- Received by editor(s): November 28, 1995
- Communicated by: James West
- © Copyright 1998 American Mathematical Society
- 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
Dedicated: Dedicated to Professor Junji Kato on his sixtieth birthday