Solution spaces of homogeneous linear difference systems with coefficient matrices from commutative groups. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Hasil, Petr; Veselý, Michal
• Is Part Of: Journal of difference equations and applications. Volume 23:Issue 8(2017)
• Page Start: 1324
• Page End: 1353
• Publication Date: 2017-08-03
• Subjects: Limit periodicity -- almost periodicity -- almost periodic sequences -- almost periodic solutions -- linear difference equations; 39A06 -- 39A24 -- 42A75 -- 43A60 -- 65Q10; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2017.1326912
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract: We analyse the solution spaces of limit periodic homogeneous linear difference systems, where the coefficient matrices of the considered systems are taken from a commutative group which does not need to be bounded. In particular, we study such systems whose fundamental matrices are not asymptotically almost periodic or which have solutions vanishing at infinity. We identify a simple condition on the matrix group which guarantees that the studied systems form a dense subset in the space of all considered systems. The obtained results improve previously known theorems about non-almost periodic and non-asymptotically almost periodic solutions. Note that the elements of the coefficient matrices are taken from an infinite field with an absolute value and that the corresponding almost periodic case is treated as well.