A new view of the lp-theory for a system of higher order difference equations

It is proved under appropriate assumptions that the solutions of a linear system of higher order difference equations belong to lp, that is the pth powers of the solutions are summable for some p 1. Our results are based on a new transformation of the higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. Our theory is illustrated by examples, including an interesting exponential stability result and a class of linear delay difference equations.