Bohr conditions and almost periodic means in quasi-complete spaces

Document Type : Dedicated to Prof. A. T.-M. Lau


Department of Mathematics, ‎University of Windsor, Ontario, Canada.


We study Bohr conditions for functions on topological groups taking values in locally convex spaces. We show that functions satisfying Bohr conditions are uniformly continuous. We show that in quasi-complete spaces, Bohr conditions are equivalent to Bochner's characterizations of almost periodicity. We prove the existence of invariant mean for almost periodic functions with values in quasi-complete spaces.


Main Subjects

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