Noncommutative Functional Calculus

The book contains recent results concerning a functional calulus for n-tuples of not necessarily commuting linear operators and for quaternionic linear operators. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra the so-called slice monogenic functions which are carefully described in the book and, in particular, for functions with values in the algebra of quaternions the so-called slice regular functions. All the results in the book are new (except for an Appendix on the Riesz-Dunford functional calculus and for a short introduction