Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 126, pp. 1-22.
Title: Construction of almost periodic sequences with given properties
Author: Michal Vesely (Masaryk Univ., Brno, Czech Republic)
Abstract:
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.