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Spectral Theory on the S-Spectrum for Quaternionic Operators

  • Fabrizio Colombo
  • Jonathan Gantner
  • David P. Kimsey

Part of the Operator Theory: Advances and Applications book series (OT, volume 270)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 1-10
  3. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 11-51
  4. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 53-74
  5. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 75-124
  6. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 125-136
  7. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 137-149
  8. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 151-176
  9. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 177-185
  10. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 187-217
  11. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 219-231
  12. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 233-243
  13. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 245-254
  14. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 255-271
  15. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 273-302
  16. Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 303-335
  17. Back Matter
    Pages 337-356

About this book

Introduction

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

Keywords

S-spectrum S-functional calculus F-functional calculus quaternionic spectral theorem spectral integration spectral operators slice hyperholomorphic functions

Authors and affiliations

  • Fabrizio Colombo
    • 1
  • Jonathan Gantner
    • 2
  • David P. Kimsey
    • 3
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  3. 3.School of Mathematics, Statistics & PhysicsNewcastle UniversityNewcastle upon TyneUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-03074-2
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-03073-5
  • Online ISBN 978-3-030-03074-2
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site