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Slice Hyperholomorphic Functional Calculi

In: Operator Theory

Author

Listed:
  • Fabrizio Colombo

    (Politecnico di Milano, Dipartimento di Matematica)

  • Irene Sabadini

    (Politecnico di Milano, Dipartimento di Matematica)

Abstract

This paper is a survey on some functional calculi constructed with slice hyperholomorphic functions, mainly on the S-functional calculus. This is a functional calculus, defined for n-tuples of not necessarily commuting operators, and it is based on the recent theory of slice hyperholomorphic functions. Its version for commuting operators, called the SC-functional calculus, and its quaternionic version, called the quaternionic functional calculus, are presented, as well as the so-called F-functional calculus, based on the Fueter–Sce mapping theorem in integral form.Since the theory of hyperholomorphic functions is quite recent, the paper contains the main results of this function theory that are necessary to introduce these calculi, as well as the Fueter–Sce mapping theorem in integral form.

Suggested Citation

  • Fabrizio Colombo & Irene Sabadini, 2015. "Slice Hyperholomorphic Functional Calculi," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 63, pages 1787-1821, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_21
    DOI: 10.1007/978-3-0348-0667-1_21
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