Twin semigroups and delay equations

In the standard theory of delay equations, fundamental solution does not ‘live’ in state space. To eliminate this age-old anomaly, we enlarge As a consequence, lose strong continuity operators and this, turn, has as consequence that Riemann integral no longer suffices for giving meaning to variation-of-constants formula. compensate, develop Stieltjes-Pettis setting norming dual pair spaces. Part I provides general theory, II deals with “retarded” III show how Stieltjes enables incorporation unbounded perturbations corresponding neutral equations.