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Spectral Theory on the S-Spectrum for Quaternionic Operators

  • Book
  • © 2018

Overview

Authors:
  1. Fabrizio Colombo

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  2. Jonathan Gantner

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  3. David P. Kimsey

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

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  • Presents original research previously unpublished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
    Download chapter PDF

  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
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Keywords

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

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