Eigenvalues of some almost periodic functions

Egawa, Jirō

doi:10.1090/S0002-9939-1992-1079890-3

Eigenvalues of some almost periodic functions
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Proc. Amer. Math. Soc. 115 (1992), 535-540 Request permission

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 \[ d(f,g) = \sup \limits _{t \in R} |f(t) - g(t)|.\] 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

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Topological groups

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