Noncommutative Functional Calculus

Theory and Applications of Slice Hyperholomorphic Functions

  • Fabrizio Colombo
  • Irene Sabadini
  • Daniele C. Struppa

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

  • Fabrizio Colombo
    • 1
  • Irene Sabadini
    • 2
  • Daniele C. Struppa
    • 3
  1. 1., Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2., Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3., Schmid College of ScienceChapman UniversityOrangeUSA

Bibliographic information

  • 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
  • Print ISBN 978-3-0348-0109-6
  • Online ISBN 978-3-0348-0110-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • About this book