On the Fueter-Sce theorem and Cauchy-Kovalevskaya extensions over alternative $\ast$-algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918390378004480 |
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| author | Huo, Qinghai Sabadini, Irene Xu, Zhenghua |
| author_facet | Huo, Qinghai Sabadini, Irene Xu, Zhenghua |
| contents | Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized partial-slice monogenic functions defined on hypercomplex subspaces and with values in a real alternative $\ast$-algebra and we concentrate on the Fueter-Sce theorem, three types of Cauchy-Kovalevskaya extensions, and their various internal relationships. The paper proposes more bridges between the theories of monogenicity, harmonicity, and generalized partial-slice monogenicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15014 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Fueter-Sce theorem and Cauchy-Kovalevskaya extensions over alternative $\ast$-algebras Huo, Qinghai Sabadini, Irene Xu, Zhenghua Complex Variables Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized partial-slice monogenic functions defined on hypercomplex subspaces and with values in a real alternative $\ast$-algebra and we concentrate on the Fueter-Sce theorem, three types of Cauchy-Kovalevskaya extensions, and their various internal relationships. The paper proposes more bridges between the theories of monogenicity, harmonicity, and generalized partial-slice monogenicity. |
| title | On the Fueter-Sce theorem and Cauchy-Kovalevskaya extensions over alternative $\ast$-algebras |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.15014 |