Noncommutative Functional Calculus
Description
<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>
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.
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Content
1 Introduction.- 2 Slice monogenic functions.- 3 Functional calculus for n -tuples of operators.- 4 Quaternionic Functional Calculus.- 5 Appendix: The Riesz-Dunford functional calculus.- Bibliography.- Index.
