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Functions and Operators in Real, Quaternionic, and Cliffordian Contexts

In: Multivariable Operator Theory

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Listed:
  • Florian-Horia Vasilescu

    (University of Lille, Department of Mathematics)

Abstract

This is an expository paper mainly based on certain works due to the author himself. After some introductory sections, we discuss the transformation of vector valued stem functions, defined on sets in the complex plane into quaternionic and Cliffordian valued function, using functional calculi, algebraically or derived via a Cauchy type kernel. Then we consider large families of quaternionic and Cliffordian linear operators, regarded as special classes of real linear operators, extended via a complexification procedure, and thus having the spectrum in the complex plane, which permits the construction of functional calculi with adequate analytic functions, in a classical manner, recaptured by restriction.

Suggested Citation

  • Florian-Horia Vasilescu, 2023. "Functions and Operators in Real, Quaternionic, and Cliffordian Contexts," Springer Books, in: Ernst Albrecht & Raúl Curto & Michael Hartz & Mihai Putinar (ed.), Multivariable Operator Theory, pages 833-860, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50535-5_30
    DOI: 10.1007/978-3-031-50535-5_30
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