A unified notion of regularity in one hypercomplex variable
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917687175675904 |
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| author | Ghiloni, Riccardo Stoppato, Caterina |
| author_facet | Ghiloni, Riccardo Stoppato, Caterina |
| contents | We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02891 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A unified notion of regularity in one hypercomplex variable Ghiloni, Riccardo Stoppato, Caterina Complex Variables 30G35 We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over quaternions, in addition to subsuming the notions of Fueter-regular function and of slice-regular function, it gives rise to an entirely new theory, which we develop in some detail. |
| title | A unified notion of regularity in one hypercomplex variable |
| topic | Complex Variables 30G35 |
| url | https://arxiv.org/abs/2309.02891 |