  In this work, we present a novel approach to the mathematical analysis of
equations with memory based on the notion of a state, namely, the initial
configuration of the system which can be unambiguously determined by the
knowledge of the future dynamics. As a model, we discuss the abstract version
of an equation arising from linear viscoelasticity. It is worth mentioning that
our approach goes back to the heuristic derivation of the state framework,
devised by L.Deseri, M.Fabrizio and M.J.Golden in "The concept of minimal state
in viscoelasticity: new free energies and applications to PDEs", Arch. Ration.
Mech. Anal., vol. 181 (2006) pp.43-96. Starting from their physical
motivations, we develop a suitable functional formulation which, as far as we
know, is completely new.
