Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909201330077696 |
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| author | Li, Yong |
| author_facet | Li, Yong |
| contents | In this article we will give a affirmative answer to Gilbert's conjecture on Hardy spaces of Clifford analytic functions in upper half-space of $\mathbb{R}^8$. It depends on a explicit construction of Spinor space $\mathcal{R}_8$ and Clifford algebra $Cl_8$ by octonion algbra. What's more , it gives us an associative way to octonionic analytic function theory. And the similar question has been discussed in Octonionic Hardy space in upper-half space, some classical results about octonionic analytic functions have been reformulated, too. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_14164 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis Li, Yong Complex Variables 30A05, 30G35, 30H10, 42B30 In this article we will give a affirmative answer to Gilbert's conjecture on Hardy spaces of Clifford analytic functions in upper half-space of $\mathbb{R}^8$. It depends on a explicit construction of Spinor space $\mathcal{R}_8$ and Clifford algebra $Cl_8$ by octonion algbra. What's more , it gives us an associative way to octonionic analytic function theory. And the similar question has been discussed in Octonionic Hardy space in upper-half space, some classical results about octonionic analytic functions have been reformulated, too. |
| title | Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis |
| topic | Complex Variables 30A05, 30G35, 30H10, 42B30 |
| url | https://arxiv.org/abs/2306.14164 |