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© 2011

Noncommutative Functional Calculus

Theory and Applications of Slice Hyperholomorphic Functions

Book

Part of the Progress in Mathematics book series (PM, volume 289)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
    Pages 1-16
  3. Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
    Pages 17-80
  4. Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
    Pages 81-112
  5. Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
    Pages 113-200
  6. Fabrizio Colombo, Irene Sabadini, Daniele C. Struppa
    Pages 201-210
  7. Back Matter
    Pages 211-221

About this book

Introduction

<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>

<br> 

<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>

Keywords

Riesz-Dunford functional calculus spectral theory theory of slice hyperholomorphic functions

Authors and affiliations

  1. 1., Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2., Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3., Schmid College of ScienceChapman UniversityOrangeUSA

Bibliographic information

  • Book Title Noncommutative Functional Calculus
  • Book Subtitle Theory and Applications of Slice Hyperholomorphic Functions
  • Authors Prof. Fabrizio Colombo Politecnico di Milano
    Irene Sabadini
    Daniele C. Struppa
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-0110-2
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0109-6
  • Softcover ISBN 978-3-0348-0324-3
  • eBook ISBN 978-3-0348-0110-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages VI, 222
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
    Functional Analysis
    Functions of a Complex Variable
  • Buy this book on publisher's site