Perturbing evolutionary systems on dual spaces by cumulative outputs
Mats Gyllenberg, Timothy Lant, Horst R. Thieme · Differential and Integral Equations · 2006
Evolutionary systems on dual Banach spaces X = Z * are perturbed by cumulative outputs.The perturbation procedure involves solving Stieltjes operator integral equations.While either of the two operator families may or may not be formed by dual operators, the case that the output family does not consist of dual operators receives particular attention.Topologies are identified in which both the unperturbed and the perturbed evolutionary system are continuous functions of the time variables.The perturbation of the associated evolution semigroups and integrated semigroups is an important intermediate step.The perturbation results are applied to evolutionary systems acting on spaces of Borel measures on certain locally compact Hausdorff spaces and to the associated transition functions.