发表机构
Instituto Politécnico Nacional; University of Ostrava（墨西哥国立理工学院; 俄斯特拉发大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究四元数切片正则函数与富埃特超全纯函数联系，借助全局算子\(G\)、富埃特算子\(\mathcal D\)和拉普拉斯算子\(\Delta_{\mathbb{R}^{4}}\)的新关系得相关理论结果，还引入并研究了与单位球相关的超全纯函数子模。
AI 中文摘要
本文给出了切片正则函数和超全纯函数理论的一些结果，这些结果是全局算子\(G\)、富埃特算子\(\mathcal D\)和拉普拉斯算子\(\Delta_{\mathbb{R}^{4}}\)之间新关系的结果。尽管结果是在四元数环境中给出的，但切片正则函数理论的向量微积分精细解释产生了该理论与调和分析之间的有趣关系。此外，我们根据函数的新级数展开引入并研究了与单位球\(\mathbb B^4(0,1)\)相关的超全纯函数子模。
英文摘要
This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator $G$, Fueter operator $\mathcal D$ and Laplacian operator $Δ_{\mathbb{R}^{4}}$. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball $\mathbb B^4(0,1)$ given in terms of new series expansions of these functions.
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