Seminar 5. Towards the Chernoff Theorem

The main theme of this session will be methods for approximating operator semigroups. It will be shown how the convergence of generators and resolvents is related to the convergence of the semigroups themselves. As an application of this technique to a family of commuting semigroups, the classical Hille–Yosida theorem will be proved. Subsequently, the Trotter–Kato theorems, which refine the conditions for such convergence, will be presented. The final part will be a discussion of the Chernoff theorem, which represents the culmination in the study of operator semigroup approximations.