Identification problems of retarded differential systems in Hilbert spaces

Abstract

This paper deals with the identification problem for the $L^1$-valued retarded functional differential equation. The unknowns are parameters and operators appearing in the given systems. In order to identify the parameters, we introduce the solution semigroup and the structural operators in the initial data space, and provide the representations of spectral projections and the completeness of generalized eigenspaces. The sufficient condition for the identification problem is given as the so called rank condition in terms of the initial values and eigenvectors of adjoint operator.