Delay Differential Equations in Sequence Spaces

Abstract

The standard delay equations are newly studied in the context of classical separable Banach Sequence Spaces. As a classical solution is shown to exist, the associated semigroup and its infinitesimal generator are found, and some important properties of those operators are proven, including some spectral properties. As an application, it is shown how can these results be used to characterize the constrained null-controllability.