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Slice Hyperholomorphic Functions

  • Fabrizio Colombo
  • Jonathan Gantner
  • David P. Kimsey
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 270)

Abstract

We will develop operator theory for quaternionic linear operators using the theory of slice hyperholomorphic functions. The most important results are the structure formula (or representation formula) and the Cauchy formulas with slice hyperholomorphic integral kernels. We will discuss the two Cauchy formulas and the associated Cauchy kernels in detail because they are the starting point for defining the S-functional calculus (in the quaternionic setting the S-functional calculus is often called the quaternionic functional calculus).

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Fabrizio Colombo
    • 1
  • Jonathan Gantner
    • 1
  • David P. Kimsey
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.School of Mathematics, Statistics & PhysicsNewcastle UniversityNewcastle upon TyneUK

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