This book presents a functional calculus for n-tuples of not
necessarily commuting linear operators. In particular, a functional
calculus for quaternionic linear operators is developed. 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. In the case of functions with
values in the algebra of quaternions these functions are named slice
regular functions.
Except for the appendix and the introduction all results are new and
appear for the first time organized in a monograph. The material has
been carefully prepared to be as self-contained as possible. The
intended audience consists of researchers, graduate and postgraduate
students interested in operator theory, spectral theory, hypercomplex
analysis, and mathematical physics.