Almost periodic sequences and functions with given values. (English) Zbl 1240.11088
The author presents a special method of constructing of almost periodic sequences and functions attaining values in a metric space. Using this construction, it is shown, among others, that for any countable totally bounded set \(X\) in a metric space there exists an almost periodic sequence \(\{\psi _k\}_{k\in \mathbb {Z}}\) such that \(X=\{\psi _k,\, k\in \mathbb {Z}\}\) and \(\psi _k\) satisfies \(\psi _k=\psi _k+lq(k)\) for all \(k\) and some \(q(k)\) which depends on \(k\).
Reviewer: Ondřej Došlý (Brno)
MSC:
11K70 | Harmonic analysis and almost periodicity in probabilistic number theory |
11K31 | Special sequences |
42A75 | Classical almost periodic functions, mean periodic functions |
43A60 | Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions |
46S40 | Fuzzy functional analysis |