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Structural properties of functional differential equations in Banach spaces. (English) Zbl 0713.34069
The treatment of functional differential equations in the state space $${\mathbb{R}}^ n\times L^ p([-n,0],{\mathbb{R}}^ n)$$ initiated by C. Bernier and 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.
Reviewer: R.Nagel

##### MSC:
 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34G10 Linear differential equations in abstract spaces 47D06 One-parameter semigroups and linear evolution equations