Generalized partial-slice monogenic functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908166498811904 |
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| author | Xu, Zhenghua Sabadini, Irene |
| author_facet | Xu, Zhenghua Sabadini, Irene |
| contents | The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03698 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized partial-slice monogenic functions Xu, Zhenghua Sabadini, Irene Complex Variables The two function theories of monogenic and of slice monogenic functions have been extensively studied in the literature and were developed independently; the relations between them, e.g. via Fueter mapping and Radon transform, have been studied. The main purpose of this article is to describe a new function theory which includes both of them as special cases. This theory allows to prove nice properties such as the identity theorem, a Representation Formula, the Cauchy (and Cauchy-Pompeiu) integral formula, the maximum modulus principle, a version of the Taylor and Laurent series expansions. As a complement, we shall also offer two approaches to these functions via slice functions and via global differential operators. In addition, we discuss the conformal invariance property under a proper group of Möbius transformations preserving the partial symmetry of the involved domains. |
| title | Generalized partial-slice monogenic functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2309.03698 |