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  • © 2018

Spectral Theory on the S-Spectrum for Quaternionic Operators

Birkhäuser
  • Presents original research previously unpublished
  • Closes a gap in research
  • Develops quaternionic spectral theory

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

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-ix
  2. Introduction

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 1-10
  3. Slice Hyperholomorphic Functions

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 11-51
  4. The S-Spectrum and the S-Functional Calculus

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 53-74
  5. Properties of the S-Functional Calculus for Bounded Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 75-124
  6. The S-Functional Calculus for Unbounded Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 125-136
  7. The H-Functional Calculus

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 137-149
  8. The F-Functional Calculus for Bounded Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 151-176
  9. The F-Functional Calculus for Unbounded Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 177-185
  10. Quaternionic Operators on a Hilbert Space

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 187-217
  11. Spectral Integrals

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 219-231
  12. The Spectral Theorem for Bounded Normal Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 233-243
  13. The Spectral Theorem for Unbounded Normal Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 245-254
  14. Spectral Theorem for Unitary Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 255-271
  15. Spectral Integration in the Quaternionic Setting

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 273-302
  16. Bounded Quaternionic Spectral Operators

    • Fabrizio Colombo, Jonathan Gantner, David P. Kimsey
    Pages 303-335
  17. Back Matter

    Pages 337-356

About this book

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.

Authors and Affiliations

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Fabrizio Colombo, Jonathan Gantner

  • School of Mathematics, Statistics & Physics, Newcastle University, Newcastle upon Tyne, UK

    David P. Kimsey

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access