Structural properties of functional differential equations in Banach spaces (Q749745)

The treatment of functional differential equations in the state space \({\mathbb{R}}^ n\times L^ p([-n,0],{\mathbb{R}}^ n)\) initiated by \textit{C. Bernier} and \textit{A. Manitius} [Can. J. Math. 30, 897-914 (1978; Zbl 0368.47026)] is extended to Banach space valued equations. The associated semigroups and the structural operators are investigated and a spectral theory including the completeness of generalized eigenfunctions is developped. Applications to partial differential equations with delay conclude the paper.