Noncommutative Functional Calculus : Theory and Applications of Slice Hyperholomorphic Functions
Operator theory Functional analysis Functions of complex variables Functions of a Complex Variable
Imprint: Birkhäuser
2011
1st ed. 2011.
EISBN 1283086484
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.
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.
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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.
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.
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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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