Abstract:
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.
