Norm continuity of solution semigroups of a class of neutral functional differential equations with distributed delay

In this note, we shall consider the norm continuity of a class of solution semigroups associated with linear functional differential equations of neutral type with time lag r>0 in Hilbert spaces. The norm continuity plays an important role in the analysis of asymptotic stability of the system under consideration by means of spectrum approaches. We shall show that for a square integrable neutral delay term and an unbounded infinitesimal generator A multiplied by a square integrable weight function in the distributed delay term, the associated solution semigroup of the system is norm continuous at every t>r.