Difference operators as semigroup generators

In this paper we examine difference operators with constant coefficients. We show that the type of the generated semigroup is determined by a matrix 𝔹 , originating from the domain of the operator. Moreover, we provide necessary and sufficient conditions for exponential and polynomial stability of the semigroup in terms of the matrix 𝔹 , using results of A. Borichev and Y. Tomilov. We close the paper with an application of our results to flows in networks.