Necessary and sufficient condition for the unique existence of periodic solution of linear volterra equations

In this paper, we obtained the sufficient and necessary condition for the unique existence of periodic solution of the linear Volterra integro-differential equations of the form $$x'(t) = \int_0^\infty {(dE(s))x(t - s) + f(t)} $$ . We also proved that the mentioned equation has unique periodic solution is a generic property.