标题： 离散八元数分析：一种统一处理分裂八元数和经典情况的方法 显示英文标题

标题： Discrete octonionic analysis: a unified approach to the split-octonionic and classical settings

摘要： 数学物理中的各种问题将八元数和分裂八元数视为一种数学结构，这种结构构成了这些问题的八维性质。 因此，近年来八元数分析已成为一个活跃的研究领域。 八元数分析的主要目标之一是开发一种八元数算子微积分工具，用于解决受益于使用八元数结构的数学物理边界值问题。 然而，当我们想在实践中应用算子微积时，很明显需要定义连续构造的适当离散对应物。 在以前的工作中，我们已经提出了几种对经典连续八元数分析进行离散化的方法。 然而，分裂八元数的情况，这在近年来具体研究中对于实际应用尤为重要，直到现在还没有被考虑过。 因此，本文的目标之一是解释如何特别处理离散的分裂八元数设置。 此外，我们提出了一种通用框架，以一种统一的方法涵盖所有不同的离散八元数设置，同时也涵盖了不同的八维代数结构。 显示英文摘要

摘要： Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become an area of active research in recent years. One of the main goals of octonionic analysis is to develop tools of an octonionic operator calculus for solving boundary value problems of mathematical physics that benefit from the use of the octonionic structure. However, when we want to apply the operator calculus in practice, it becomes evident that adequate discrete counterparts of continuous constructions need to be defined. In previous works, we have proposed several approaches to discretise the classical continuous octonionic analysis. However, the split-octonionic case, which is particularly important for practical applications concretely investigated in the last years, has not been considered until now. Therefore, one of the goals of this paper is to explain how to particularly address the discrete split-octonionic setting. Additionally, we propose a general umbrella to cover all different discrete octonionic settings in one unified approach that also encompasses the different eight-dimensional algebraic structures.