Cullen-regular quaternionic functions in a Fueter operator framework

Abstract

We show characterizations of the class of Cullen-regular functions in the sense of Gentili-Struppa for any domain $\Omega$ in terms of the Fueter operator. We then state a Integral Theorem and discuss how it can be used to define a more general version of Cullen-regularity, that does not require the function to be of class $C^1$.

References in corpus (1)

• A generalization of Fueter's Theorem

Cited by in corpus (2)

• Semiweak Cullen-regular quaternionic functions
• The quaternionic Cullen-regular product for a larger class of functions