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Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes

Birkhäuser
  • Contains a new theory for evolution operators
  • Allows defining new classes of fractional diffusion and evolution problems
  • Inspires to explore new research directions

Part of the book series: Operator Theory: Advances and Applications (OT, volume 274)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-viii
  2. Introduction

    • Fabrizio Colombo, Jonathan Gantner
    Pages 1-15
  3. Preliminary results

    • Fabrizio Colombo, Jonathan Gantner
    Pages 17-44
  4. The direct approach to the S-functional calculus

    • Fabrizio Colombo, Jonathan Gantner
    Pages 45-104
  5. The Quaternionic Evolution Operator

    • Fabrizio Colombo, Jonathan Gantner
    Pages 105-131
  6. Perturbations of the generator of a group

    • Fabrizio Colombo, Jonathan Gantner
    Pages 133-150
  7. The Phillips functional calculus

    • Fabrizio Colombo, Jonathan Gantner
    Pages 151-172
  8. The H-Functional Calculus

    • Fabrizio Colombo, Jonathan Gantner
    Pages 173-211
  9. Fractional powers of quaternionic linear operators

    • Fabrizio Colombo, Jonathan Gantner
    Pages 213-250
  10. The fractional heat equation using quaternionic techniques

    • Fabrizio Colombo, Jonathan Gantner
    Pages 251-265
  11. Applications to fractional diffusion

    • Fabrizio Colombo, Jonathan Gantner
    Pages 267-284
  12. Historical notes and References

    • Fabrizio Colombo, Jonathan Gantner
    Pages 285-300
  13. Appendix: Principles of functional Analysis

    • Fabrizio Colombo, Jonathan Gantner
    Pages 301-306
  14. Back Matter

    Pages 307-322

About this book

This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. 

These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields.

This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey  (Operator Theory: Advances and Applications, Vol. 270).


Authors and Affiliations

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

    Fabrizio Colombo, Jonathan Gantner

Bibliographic Information

  • Book Title: Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes

  • Authors: Fabrizio Colombo, Jonathan Gantner

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-030-16409-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-16408-9Published: 25 July 2019

  • Softcover ISBN: 978-3-030-16411-9Published: 14 August 2020

  • eBook ISBN: 978-3-030-16409-6Published: 10 July 2019

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: VIII, 322

  • Topics: Operator Theory

Buy it now

Buying options

eBook USD 39.99 USD 79.99
50% discount Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99 USD 99.99
50% discount Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 69.99 USD 129.99
46% discount 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