Remarks on linear Volterra integral equations of parabolic type (Q1070480)

The author proves some existence, uniqueness and regularity results referring to a Volterra integral equation of parabolic type, i.e., to an equation of the form \[ u(t)+\int^{t}_{0}b(t-s)A(s)u(s)=f(t),0\leq t\leq T, \] where b is a complex-valued function with \(b(0)=1\), while, for each t,-A(t) generates an analytic semigroup in a Banach space X.