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Proceedings of the American Mathematical Society

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Eigenvalues of some almost periodic functions


Author: Jirō Egawa
Journal: Proc. Amer. Math. Soc. 115 (1992), 535-540
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9939-1992-1079890-3
MathSciNet review: 1079890
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Abstract: Let $ {B_U}$ be the set of real valued functions on $ R$ which are bounded and uniformly continuous. For $ f,g \in {B_U}$, put

$\displaystyle d(f,g) = \mathop {\sup }\limits_{t \in R} \vert f(t) - g(t)\vert.$

Then $ {B_U}$ becomes a metric space. On $ {B_U}$ we define a flow $ \eta $ by $ \eta (f,t) = {f_t}$ for $ (f,t) \in {B_U} \times R$. We denote the restriction of $ \eta $ to the hull of $ f \in {B_U}$ by $ {\eta _f}$. If $ f$ is almost periodic, then the set of eigenvalues of $ {\eta _f}$ coincides with the module of $ f$ (see J. Egawa, Eigenvalues of compact minimal flows, Math. Seminar Notes (Kobe Univ.), 10 (1982), 281-291. In this paper, we extend this result to almost periodic functions with some additional properties.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1079890-3
Keywords: Equicontinuous, minimal flow, almost periodic function, eigenvalues
Article copyright: © Copyright 1992 American Mathematical Society