Abstract. In order to solve the identifiability problem for the partial functional differential equation: $$ u_t(t,x) = u_{xx} (t,x)+b u(t,x) +c u_{xx} (t-h,x) + \int_{-h}^0 a(s) u_{xx} (t+s,x) ds $$ we consider the abstract functional differential equation $u'(t)=A u(t)+B u(t)+L(u_t)$ in the Hilbert space $X$. We study eigenspaces of the infinitesimal generators of the solution and the adjoint semigroups. By using structural operators, eigenspaces of the generator of adjoint semigroup are characterized, and the identifiability of parameters for a given partial functional differential equation is obtained.

AMS Subject Classification (1991): 34G10, 34K30, 47D03

Received June 27, 2001, and in revised form March 28, 2002. (Registered under 2888/2009.)