Noncommutative Functional Calculus
Theory and Applications of Slice Hyperholomorphic Functions
Authors: Colombo, Fabrizio, Sabadini, Irene, Struppa, Daniele C.
Free Preview- <p>This book shows that the Riesz-Dunford functional calculus can be extended to n-tuples of not necessarily commuting operators. To do so, the authors develop a completely new spectral theory.</p>
- <p>The fundamental technical tools is the newly developed theory of slice hyperholomorphic functions (which includes functions of a paravector variable with values in a Clifford algebra and quaternionic valued functions of a quaternionic variable).</p>
- <p>The monograph is based on results by the authors and thus it is completely original, except for a few pages of basic material and an Appendix.</p>
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- About this book
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<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 (5 chapters)
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Introduction
Pages 1-16
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Slice monogenic functions
Pages 17-80
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Functional calculus for n-tuples of operators
Pages 81-112
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Quaternionic Functional Calculus
Pages 113-200
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Appendix: The Riesz–Dunford functional calculus
Pages 201-210
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Table of contents (5 chapters)
- Download Preface 1 PDF (86.4 KB)
- Download Sample pages 1 PDF (1,019.6 KB)
- Download Table of contents PDF (56.5 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Noncommutative Functional Calculus
- Book Subtitle
- Theory and Applications of Slice Hyperholomorphic Functions
- Authors
-
- Fabrizio Colombo
- Irene Sabadini
- Daniele C. Struppa
- Series Title
- Progress in Mathematics
- Series Volume
- 289
- Copyright
- 2011
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Basel AG
- eBook ISBN
- 978-3-0348-0110-2
- DOI
- 10.1007/978-3-0348-0110-2
- Hardcover ISBN
- 978-3-0348-0109-6
- Softcover ISBN
- 978-3-0348-0324-3
- Series ISSN
- 0743-1643
- Edition Number
- 1
- Number of Pages
- VI, 222
- Topics
