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On Bohr almost periodicity

Published online by Cambridge University Press:  24 October 2008

Paul Milnes
Paul Milnes
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ont. N6A 5B7, Canada
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Abstract

The first examples of Bohr almost periodic functions that are not almost periodic were given by T. -S. Wu. Later, the present author showed that Bohr almost periodic functions could be distal (and not almost periodic) and even merely minimal. Here it is proved that all Bohr almost periodic functions are minimal. The proof yields an unusual feature about the orbit of a Bohr almost periodic function, one which does not characterize Bohr almost periodic functions, but can be used to show that a Bohr almost periodic function f that is point distal must be distal or, if f is almost automorphic, it must be almost periodic. Some pathologies of Bohr almost periodic functions are discussed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 489 - 493
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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