A criterion for the exponential stability of linear difference equations Original Research Article

We give an affirmative answer to a question formulated by Aulbach and Van Minh by showing that the linear difference equation xn+1=Anxn,forn∈Nxn+1=Anxn,forn∈N Turn MathJax on in a Banach space B is exponentially stable if and only if for every f = {fn}n=1∞ ∈ lp(NNB), where I < p < ∞, the solution of the Cauchy problem xn+1=Anxn+fn,forn∈N,x1=0xn+1=Anxn+fn,forn∈N,x1=0 Turn MathJax on is bounded on NN.