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arXiv · 2401.04401

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

Xinyuan Dou·Ming Jin·Guangbin Ren·Ting Yang
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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.

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Xinyuan Dou, Ming Jin, Guangbin Ren, Ting Yang. 2024-01-09. Path-slice star-product on non-axially symmetric domains in several quaternionic variables. https://arxiv.org/abs/2401.04401

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