
Noncommutative Functional Calculus
Theory and Applications of Slice Hyperholomorphic Functions
von Prof. Fabrizio Colombo Politecnico di Milano, Irene Sabadini und Daniele C. Struppa< i> This book presents a functional calculus for < i> n</i>-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.</i>
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< p> 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.</p>