Overview
- 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.
- 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).
- 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.
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 289)
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Table of contents (5 chapters)
Keywords
About this book
<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>
Authors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-0348-0110-2
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Hardcover ISBN: 978-3-0348-0109-6Published: 23 March 2011
Softcover ISBN: 978-3-0348-0324-3Published: 21 April 2013
eBook ISBN: 978-3-0348-0110-2Published: 18 March 2011
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: VI, 222
Topics: Operator Theory, Functional Analysis, Functions of a Complex Variable