Progress in Mathematics

Noncommutative Functional Calculus

Theory and Applications of Slice Hyperholomorphic Functions

Authors: Colombo, Fabrizio, Sabadini, Irene, Struppa, Daniele C.

  • <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

<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)

  • Introduction

    Colombo, Fabrizio (et al.)

    Pages 1-16

  • Slice monogenic functions

    Colombo, Fabrizio (et al.)

    Pages 17-80

  • Functional calculus for n-tuples of operators

    Colombo, Fabrizio (et al.)

    Pages 81-112

  • Quaternionic Functional Calculus

    Colombo, Fabrizio (et al.)

    Pages 113-200

  • Appendix: The Riesz–Dunford functional calculus

    Colombo, Fabrizio (et al.)

    Pages 201-210

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-0348-0110-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-0348-0109-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-0348-0324-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Noncommutative Functional Calculus
Book Subtitle
Theory and Applications of Slice Hyperholomorphic Functions
Authors
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