Path-slice star-product on non-axially symmetric domains in several quaternionic variables
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914635364433920 |
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| author | Dou, Xinyuan Jin, Ming Ren, Guangbin Yang, Ting |
| author_facet | Dou, Xinyuan Jin, Ming Ren, Guangbin Yang, Ting |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Path-slice star-product on non-axially symmetric domains in several quaternionic variables Dou, Xinyuan Jin, Ming Ren, Guangbin Yang, Ting Complex Variables Primary: 30G35, Secondary: 32A30 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. |
| title | Path-slice star-product on non-axially symmetric domains in several quaternionic variables |
| topic | Complex Variables Primary: 30G35, Secondary: 32A30 |
| url | https://arxiv.org/abs/2401.04401 |