Structural Operators and Eigenmanifold Decomposition for Functional Differential Equations in Hilbert Spaces

This paper studies spectral properties of linear retarded functional differential equations in Hilbert spaces with the emphasis on their relations to structural operators. The equations involve unbounded operators acting on the discrete and distributed delayed terms, and the operators acting on the instantaneous term are defined through sesquilinear forms. The main concern of this paper is studying the spectral properties of the infinitesimal generators associated with the solution semigroups by means of structural operators. The characterizations of eigenmanifolds are derived and the relations between the manifolds and structural operators are shown by using the properties of structural operators.