Skew analysis over quaternions. I

TL;DR

This paper introduces skew regularity for quaternion-valued functions, showing it aligns with slice regularity on symmetric domains, and generalizes existing results while presenting new findings in the theory of slice-regular functions.

Contribution

It defines skew regularity for quaternion functions and proves its equivalence to slice regularity, extending known results to more general domains and offering new insights.

Findings

Skew regularity coincides with slice regularity on symmetric domains

Generalization of slice-regular function results to skew-regular functions

Introduction of new results in the theory of slice-regular functions

Abstract

We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over symmetric slice domains. Known results regarding slice-regular functions over symmetric slice domains are generalized to skew-regular functions over general symmetric domains. Furthermore, we present new results concerning slice-regular functions.