Construction of almost periodic functions with given properties

Abstract

We define almost periodic functions with values in a pseudometric space $mathcal{X}$. We mention the Bohr and the Bochner definition of almost periodicity. We present one modifiable method for constructing almost periodic functions in $mathcal{X}$. Applying this method, we prove that in any neighbourhood of an almost periodic skew-Hermitian linear differential system there exists a system which does not possess a nontrivial almost periodic solution.