Monogenic functions over real alternative *-algebras: the several hypercomplex variables case
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909047961157632 |
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| author | Xu, Zhenghua Ding, Chao Wang, Haiyan |
| author_facet | Xu, Zhenghua Ding, Chao Wang, Haiyan |
| contents | The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Monogenic functions over real alternative *-algebras: the several hypercomplex variables case Xu, Zhenghua Ding, Chao Wang, Haiyan Complex Variables Primary: 30G35, Secondary: 17D05, 32A26, 47G10 The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of monogenic functions over real alternative $\ast$-algebras has been introduced to unify several classical monogenic functions theories. In this paper, we initiate the study of monogenic functions of several hypercomplex variables over real alternative $\ast$-algebras, which naturally extends the theory of several complex variables to a very general setting. In this new setting, we develop some fundamental properties, such as Bochner-Martinelli formula, Plemelj-Sokhotski formula, and Hartogs extension theorem. |
| title | Monogenic functions over real alternative *-algebras: the several hypercomplex variables case |
| topic | Complex Variables Primary: 30G35, Secondary: 17D05, 32A26, 47G10 |
| url | https://arxiv.org/abs/2506.08307 |