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Construction of almost periodic sequences with given properties. (English) Zbl 1165.39014
Summary: We define almost periodic sequences with values in a pseudometric space X and we modify the Bochner definition of almost periodicity so that it remains equivalent with the Bohr definition. Then, we present one (easily modifiable) method for constructing almost periodic sequences in X. Using this method, we find almost periodic homogeneous linear difference systems that do not have any non-trivial almost periodic solution. We treat this problem in a general setting where we suppose that entries of matrices in linear systems belong to a ring with a unit.
MSC:
39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
42A75Classical almost periodic functions, mean periodic functions