# Some results on the F-functional calculus

**Fabrizio Colombo**, Politecnico di Milano, Italy

In this talk we introduce the two possible formulations of the F-functional calculus
which are based on the Fueter-Sce mapping theorem in integral form.
In the case of dimension $3$
we show that there exists the F-resolvent equation
and we study the analogue of the Riesz projectors associated with this calculus.
Moreover, we show that it is possible to define this calculus
also for $n$-tuples of unbounded operators and we obtain an integral representation formula analogous to
the one of the Riesz-Dunford functional calculus for unbounded operators acting on a complex Banach space.