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.