Norm continuity and stability for a functional differential equation in Hilbert space

A functional differential equation in Hilbert space with initial data on [−h, 0] is considered. An unbounded operator A and a square integrable weight function are acting in the distributed delay term. For a not necessarily continuous weight function the norm continuity of the associated solution semigroup is established at everyt >h. In the case that the spectrum of A is real and negative, the asymptotic stability of the solution is obtained.  2002 Elsevier Science (USA). All rights reserved