A note on temporal regularity of second order difference equations

This work deals with the study of maximal ?^p‐regularity of a pair (A,B) of bounded linear operators on a complex Banach space associated to the second order difference equation u_{n + 2} = Bu_{n + 1} + Au_n + f_n, where f is a given sequence on . We obtain results of characterization based on spectral analysis of the discrete sine family, which is the resolvent family of this equation.