Duality theory for solutions to Volterra integral equations
Consider the equation \[ u(t)=u_0+\int ^t_0 a(t-s)Au(s) ds \] in a Banach space setting. Here \(a\in L^1_{\text{loc}}(R^{+})\), positive for small \(t\), and \(A\) is linear, closed, and densely defined. The author investigates the Favard class of \(A\) and the related sun dual. Results from the duality and sun theory for semigroups are carried over to solution families for Volterra equations. Possible applications to regularity problems for systems of elliptic equations are indicated.
scientific article; zbMATH DE number 1271515
scientific article