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.
Submitted October 9, 2007. Published September 10, 2008.
Math Subject Classifications: 39A10, 42A75.
Key Words: keywords Almost periodic sequences; almost periodic solutions to difference systems.
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| Michal Vesely |
Department of Mathematics and Statistics, Masaryk University
Janackovo nam. 2a, CZ-602 00 Brno, Czech Republic
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