Slice Hyperholomorphic Functions
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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