Slice regular holomorphic Cliffordian functions of order $k$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916708081467392 |
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| author | Binosi, Giulio |
| author_facet | Binosi, Giulio |
| contents | Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}Δ^k$. When $\overline{\partial}Δ^k$ is applied to functions defined on the paravector space of some Clifford Algebra $\mathbb{R}_m$ with an odd number of imaginary units, the Fueter-Sce construction establish a critical index $k=\frac{m-1}{2}$ (sometimes called Fueter-Sce exponent) for which the class of slice regular functions is contained in the one of holomorphic Cliffordian functions of order $\frac{m-1}{2}$. In this paper we analyze the case $k<\frac{m-1}{2}$ and we find that the polynomials of degree at most $2k$ are the only slice regular holomorphic Cliffordian functions of order $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slice regular holomorphic Cliffordian functions of order $k$ Binosi, Giulio Complex Variables 30G35 30E20 Holomorphic Cliffordian functions of order $k$ are functions in the kernel of the differential operator $\overline{\partial}Δ^k$. When $\overline{\partial}Δ^k$ is applied to functions defined on the paravector space of some Clifford Algebra $\mathbb{R}_m$ with an odd number of imaginary units, the Fueter-Sce construction establish a critical index $k=\frac{m-1}{2}$ (sometimes called Fueter-Sce exponent) for which the class of slice regular functions is contained in the one of holomorphic Cliffordian functions of order $\frac{m-1}{2}$. In this paper we analyze the case $k<\frac{m-1}{2}$ and we find that the polynomials of degree at most $2k$ are the only slice regular holomorphic Cliffordian functions of order $k$. |
| title | Slice regular holomorphic Cliffordian functions of order $k$ |
| topic | Complex Variables 30G35 30E20 |
| url | https://arxiv.org/abs/2402.05556 |