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

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.