The [formula omitted]-functional calculus for unbounded operators.

In the recent years the theory of slice hyperholomorphic functions has become an important tool to study two functional calculi for n -tuples of operators and also for its applications to Schur analysis. In particular, using the Cauchy formula for slice hyperholomorphic functions, it is possible to give the Fueter–Sce mapping theorem an integral representation. With this integral representation it has been defined a monogenic functional calculus for n -tuples of bounded commuting operators, the so called F -functional calculus. In this paper we show that it is possible to define this calculus also for n -tuples containing 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. As we will see, it is not an easy task to provide the correct definition of the F -functional calculus in the unbounded case. This paper is addressed to a double audience, precisely to people with interests in hypercomplex analysis and also to people working in operator theory. [ABSTRACT FROM AUTHOR]