韦尔微积分视角在有界域离散八离子分析中的应用

Rolf Sören Kraußhar, Anastasiia Legatiuk, Dmitrii Legatiuk
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引用次数: 0

摘要

在本文中,我们提出了一种基于韦尔微积分的方法来研究$\mathbb{R}^{8}$中的有界域,从而完成了离散八分分析的基本发展。特别是,我们明确证明了有界立方体的离散斯托克斯公式,然后借助特征函数将这一结果推广到内部和外部的任意有界域。之后,我们介绍了离散内部和外部 Borel-Pompeiu 公式和 Cauchy 公式。最后,我们回顾了有界域离散八音度 Hardy 空间的构造。此外,我们明确解释了八离子乘法的非偶性在哪些地方是必要的,在哪些地方是不必要的。因此,本文完善了前几篇论文中介绍的离散八离子分析的基本框架,从而为这一领域的进一步研究提供了坚实的基础。
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Application of the Weyl calculus perspective on discrete octonionic analysis in bounded domains
In this paper, we finish the basic development of the discrete octonionic analysis by presenting a Weyl calculus-based approach to bounded domains in $\mathbb{R}^{8}$. In particular, we explicitly prove the discrete Stokes formula for a bounded cuboid, and then we generalise this result to arbitrary bounded domains in interior and exterior settings by the help of characteristic functions. After that, discrete interior and exterior Borel-Pompeiu and Cauchy formulae are introduced. Finally, we recall the construction of discrete octonionic Hardy spaces for bounded domains. Moreover, we explicitly explain where the non-associativity of octonionic multiplication is essential and where it is not. Thus, this paper completes the basic framework of the discrete octonionic analysis introduced in previous papers, and, hence, provides a solid foundation for further studies in this field.
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