Duality Theory for Solutions to Volterra Integral Equations

We study the behavior of the dual to the solution operator of the equation u t.su0q a) Au. t. with agLl1oc Rq.in a general Banach space setting. We shall construct various spaces that are well known in semigroup theory but were not available for solution operators to Volterra integral equations previously. The most prominent one will be the space X(, the sun-dual space