Noncommutative Functional Calculus: Theory and Applications of Slice Hyperholomorphic Functions

✍ Scribed by Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa (auth.)

• Publisher: Birkhäuser Basel
• Year: 2011
• Tongue: English
• Leaves: 230
• Series: Progress in Mathematics 289
• Edition: 1
• Category: Library

✦ Synopsis

<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>

✦ Table of Contents

Front Matter....Pages i-vi
Introduction....Pages 1-16
Slice monogenic functions....Pages 17-80
Functional calculus for n -tuples of operators....Pages 81-112
Quaternionic Functional Calculus....Pages 113-200
Appendix: The Riesz–Dunford functional calculus....Pages 201-210
Back Matter....Pages 211-221

✦ Subjects

Operator Theory; Functional Analysis; Functions of a Complex Variable