Summary
In the paper quoted in the title it was proved that a function on a discrete group is almost automorphic if and only if it is bounded and continuous in the Bohr topology. Here this result is extended to continuous functions on arbitrary topological groups. Taken together with a theorem of Marčenko, this implies a theorem first stated, but not proved, by Veech: a function of a real variable is continuous and almost automorphic if and only if it is bounded and Levitan almost periodic.
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Literatur
Alfsen, E.M., and P. Holm: A note on compact representations and almost periodicity in topological groups. Math. Scandinav. 10, 127–137 (1962).
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Veech, W.A.: Almost automorphic functions. Proc. nat. Acad. Sci. USA 49, 462–464 (1963).
—: Almost automorphic functions on groups. Amer. J. Math. 87, 719–751 (1965).
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Flor, P. Eine Bemerkung zu meiner Arbeit „Rhythmische Abbildungen abelscher Gruppen II“. Z. Wahrscheinlichkeitstheorie verw Gebiete 12, 73–74 (1969). https://doi.org/10.1007/BF00538524
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DOI: https://doi.org/10.1007/BF00538524