A note on temporal regularity of second order difference equations

Abstract

This work deals with the study of maximal ℓp‐regularity of a pair (A,B) of bounded linear operators on a complex Banach space double-struckX associated to the second order difference equation un + 2 = Bun + 1 + Aun + fn, where f is a given sequence on double-struckX. We obtain results of characterization based on spectral analysis of the discrete sine family, which is the resolvent family of this equation.

Maximal ℓp‐regularity of multiterm fractional equations with delay

“…In the discrete case, the first works of maximal regularity are by Blunck 20,21 . Other authors 22‐28 continued this research line by studying the existence and uniqueness of solutions for discrete systems that belong to the Lebesgue space of vector‐valued sequences (see also the recent work by Dantas 29 and the references therein where temporal regularity for second‐order difference equations is analyzed).…”