Copyright © 2009 Bogdan Sasu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give new and very general characterizations for uniform exponential dichotomy of variational difference equations in terms of the admissibility of pairs of sequence spaces over ℕ with respect to an associated control system. We establish in the variational case the connections between the admissibility of certain pairs of sequence spaces over ℕ and the admissibility of the corresponding pairs of sequence spaces over ℤ. We apply our results to the study of the existence of exponential dichotomy of linear skew-product flows.