New characterizations of exponential dichotomy and exponential stability of linear difference equations.

We give a new characterization of exponential dichotomy of linear difference equations in terms of -admissibility. The obtained result is a discrete version of the recent new result of Preda et al. [( L p , L q )-admissibility and exponential dichotomy of evolution processes on the half-plane, Integral Equations Operator Theory , 49 (2004), 405–418] on exponential dichotomy of evolution processes on the half-plane. Then we derive a new characterization of exponential stability of linear difference equations. This extends the recent new result of Pituk M. [A criterion for the exponential stability of linear difference equations, Applied Mathematics Letters , 17 (2004), 779–783] and of Aulbach and Nguyen Van Minh. [The concept of spectral dichotomy for linear difference equations II, Journal of Difference Equations and Applications , 2 (1996), 251–262]. [ABSTRACT FROM AUTHOR]