Abstract:
This session is dedicated to a further investigation of the properties of $C_0$-semigroups. The
main focus is a detailed analysis of the generator: its graph, the graph norm, and the concept
of a core. The relationship between the convergence of generators, semigroups, and
resolvents is explored. The theory of invariant subspaces is discussed separately, including
the construction of the subspace of strong continuity for an arbitrary semigroup. In conclusion,
fundamental integral formulas linking the semigroup, its generator, and the resolvent are
proved, including the Taylor formula.
