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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00620 |
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| _version_ | 1866914626133819392 |
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| author | González-Cervantes, José Oscar Bory-Reyes, Juan Sabadini, Irene |
| author_facet | González-Cervantes, José Oscar Bory-Reyes, Juan Sabadini, Irene |
| contents | The study of $ψ-$hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely null-solutions of the $ψ-$Fueter operator, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. In the setting of $(q,q')-$calculus, also known as post quantum calculus, we introduce a deformation of the $ψ-$Fueter operator written in terms of suitable difference operators, which reduces to a deformed $q$ calculus when $q'=1$. We also prove the Stokes and Borel-Pompeiu formulas in this context. This work is the first investigation of results in quaternionic analysis in the setting of the $(q,q')-$calculus theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00620 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Borel-Pompeiu formula in a $(q,q')$-model of quaternionic analysis González-Cervantes, José Oscar Bory-Reyes, Juan Sabadini, Irene Complex Variables The study of $ψ-$hyperholomorphic functions defined on domains in $\mathbb R^4$ with values in $\mathbb H$, namely null-solutions of the $ψ-$Fueter operator, is a topic which captured great interest in quaternionic analysis. This class of functions is more general than that of Fueter regular functions. In the setting of $(q,q')-$calculus, also known as post quantum calculus, we introduce a deformation of the $ψ-$Fueter operator written in terms of suitable difference operators, which reduces to a deformed $q$ calculus when $q'=1$. We also prove the Stokes and Borel-Pompeiu formulas in this context. This work is the first investigation of results in quaternionic analysis in the setting of the $(q,q')-$calculus theory. |
| title | A Borel-Pompeiu formula in a $(q,q')$-model of quaternionic analysis |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2401.00620 |