Generalized Π-operator in the theory of slice monogenic functions and applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909516648415232 |
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| author | Sun, Ziyi Ding, Chao |
| author_facet | Sun, Ziyi Ding, Chao |
| contents | The Π-operator plays an important role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. In this paper, we introduce a generalized Π-operator in the theory of slice monogenic functions, and some mapping properties of the generalized Π-operator are also introduced. Further, a left and right inverse and the adjoint operator of the generalized Π-operator are given. As an application, we introduce a slice Beltrami equation, which reduces to the classical complex Beltrami equation when the dimension is 2. We show details that the norm estimate of the generalized Π-operator can determine the existence of solutions of the slice Beltrami equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Π-operator in the theory of slice monogenic functions and applications Sun, Ziyi Ding, Chao Complex Variables 30G35, 30G20, 35A22 The Π-operator plays an important role in complex analysis, especially in the theory of generalized analytic functions in the sense of Vekua. In this paper, we introduce a generalized Π-operator in the theory of slice monogenic functions, and some mapping properties of the generalized Π-operator are also introduced. Further, a left and right inverse and the adjoint operator of the generalized Π-operator are given. As an application, we introduce a slice Beltrami equation, which reduces to the classical complex Beltrami equation when the dimension is 2. We show details that the norm estimate of the generalized Π-operator can determine the existence of solutions of the slice Beltrami equation. |
| title | Generalized Π-operator in the theory of slice monogenic functions and applications |
| topic | Complex Variables 30G35, 30G20, 35A22 |
| url | https://arxiv.org/abs/2502.20740 |