Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Path-slice star-product on non-axially symmetric domains in several quaternionic variables

Xinyuan Dou, Ming Jin, Guangbin Ren, Ting Yang

Abstract

This paper extends the $*$-product from slice analysis to weakly slice analysis in several quaternionic variables, focusing on non-axially symmetric domains. It diverges from traditional applications in axially symmetric domains to address slice regularity in more complicated cases. The approach involves redefining the $*$-product for path-slice functions, borrowing techniques from strongly slice analysis. Key to this work is the introduction of relative stem-preserving set pairs and real-path-connected sets, which help establish a direct link between path-slice functions and their stem functions. The study culminates in conditions under which weakly slice regular functions form an algebra in specific slice domains, broadening the scope of slice analysis.

Path-slice star-product on non-axially symmetric domains in several quaternionic variables

Abstract

This paper extends the -product from slice analysis to weakly slice analysis in several quaternionic variables, focusing on non-axially symmetric domains. It diverges from traditional applications in axially symmetric domains to address slice regularity in more complicated cases. The approach involves redefining the -product for path-slice functions, borrowing techniques from strongly slice analysis. Key to this work is the introduction of relative stem-preserving set pairs and real-path-connected sets, which help establish a direct link between path-slice functions and their stem functions. The study culminates in conditions under which weakly slice regular functions form an algebra in specific slice domains, broadening the scope of slice analysis.
Paper Structure (5 sections, 20 theorems, 72 equations)

This paper contains 5 sections, 20 theorems, 72 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Path-slice stem functions
  4. Star-product for path-slice functions
  5. Self-stem-preserving domains

Key Result

Proposition 3.2

Suppose $\Omega\subset\mathbb{H}_s^n$ is real-path-connected. If $f,g\in\mathcal{PS}(\Omega)$ and they share a common path-slice stem function $F\in\mathcal{PSS}(f)\cap \mathcal{PSS}(g)$, then $f$ and $g$ are identical functions, i.e., $f = g$.

Theorems & Definitions (50)

  • Definition 2.1
  • Definition 2.2
  • Definition 3.1
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • proof
  • Remark 3.4
  • Lemma 3.5
  • proof
  • ...and 40 more