One of the main problems of semigroup theory for linear operators is to decide whether a concrete operator is the generator of a semigroup and how this semigroup is represented.

One idea is to write complicated operators, as a sum of simple operators. For this reason, perturbation theory has become one of the most important topics in semigroup theory. My question is about the multi-perturbed semigroups or multiple perturbation of semigroups in a Banach space. I need a recurrent formula for a semigroup perturbed by multiple (several, i.e. more than two) bounded (in general unbounded) linear operators. I have searched for it, but only found a simple case, called the Dyson-Phillips series for a semigroup generated by A0+A1. How can we find the generalisation of this formula for a semigroup generated by A0+A1+...+An for a fixed natural n? Many thanks in advance. I am looking forward to your suggestions and recommendations on this topic.