Slice Fueter-regular functions on arbitrary domains in octonions

TL;DR

This paper extends the theory of slice Fueter-regular functions in octonions to arbitrary domains, introducing new phenomena, generalizing classical theorems, and connecting to Riemann domains.

Contribution

It introduces new technical tools and concepts, such as the CCL equivalence relation and Bers-Vekua continuation, to study slice Fueter-regular functions on arbitrary domains.

Findings

Generalized maximum modulus principle for slice Fueter-regular functions

Discovered conditional uniqueness of stem vectors

Connected the theory to Riemann domains via quotient spaces

Abstract

This paper is concerned with a class of generalized slice Fueter-regular functions on arbitrary domains in O with local stem functions. Some classical theorems such as the maximum modulus principle will be generalized to our setting. Some new phenomena such as the conditional uniqueness of stem vectors will be discovered by means of new technical tools, e.g., the CCL equivalence relation and the Bers-Vekua continuation. And a natural connection between the theory of slice Fueter-regular functions and that of Riemann domains will be revealed via the quotient space under the CCL equivalence relation.