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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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