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$$p$$-adic almost periodicity and representations. (English) Zbl 0830.46071
Summary: In the first international conference on $$p$$-adic functional analysis, the question whether it is possible to get the structure of the Banach algebra $$A_c (G)$$ of $$p$$-adic valued continuous almost periodic functions on a totally disconnected topological IB-group $$G$$ through the structure of its non-archimedean Bohr compactification $$\widehat {G}$$ was raised. We affirmatively answer this question here. This structure of $$A_c (G)$$ helps one to study the $$p$$-adic regular representation of $$G$$ using the known theory of representations for compact groups.

##### MSC:
 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis
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##### References:
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