Series expansions and small solutions for Volterra equations of convolution type (Q920272)

Necessary conditions for representability of the solutions of Volterra equations of convolution type \(x-\zeta *x=f,p\) where \(\zeta\) is an \(n\times n\)-matrix-valued function on [0,h] of bounded variation, as a series of characteristic solutions, are given. The geometric properties of the strongly continuous semigroup T(t) associated with this equation are investigated, especially, the closure of the linear hull of the system of generalized eigenfunctions of the infinitesimal generator of the semigroup T(t) is considered. Finally, it is shown the existence of a closed minimal invariant subspace of the phase space, carrying all information on the equation.