Dunkl regularity over alternative $*$-algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908805278728192 |
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| author | Binosi, Giulio Perotti, Alessandro |
| author_facet | Binosi, Giulio Perotti, Alessandro |
| contents | We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the kernel of Dunkl-Cauchy-Riemann operators. Each of these function spaces, whose elements are called Dunkl-regular functions, refines Dunkl monogenic function theory and Dunkl harmonic analysis on Euclidean spaces. This approach allows a wide variety of hypercomplex function theories to be embedded as subcases of Dunkl monogenic function theory. This paves the way for further interactions between Dunkl theory and hypercomplex analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dunkl regularity over alternative $*$-algebras Binosi, Giulio Perotti, Alessandro Complex Variables 30G35, 33C52 We characterise slice-regularity of functions over a real alternative *-algebra using operators that arise in Dunkl operator theory. We present a unifying perspective on hypercomplex analysis by defining a family of function spaces in the kernel of Dunkl-Cauchy-Riemann operators. Each of these function spaces, whose elements are called Dunkl-regular functions, refines Dunkl monogenic function theory and Dunkl harmonic analysis on Euclidean spaces. This approach allows a wide variety of hypercomplex function theories to be embedded as subcases of Dunkl monogenic function theory. This paves the way for further interactions between Dunkl theory and hypercomplex analysis. |
| title | Dunkl regularity over alternative $*$-algebras |
| topic | Complex Variables 30G35, 33C52 |
| url | https://arxiv.org/abs/2602.01907 |