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.