论文标题
八元离子单基因函数理论的差异拓扑方面
Differential topological aspects in octonionic monogenic function theory
论文作者
论文摘要
在本文中，我们将Cauchy积分公式的同源版本用于八元独立性函数，以介绍此类函数的零零和$ a $ a-points的概念。作为一个很大的新颖性，我们还解决了位于某些紧凑型零品种上的零案例。到目前为止，该案例甚至还没有在Clifford的关联分析设置中进行研究。 我们还证明了分离的零和非分离的紧凑型零集的八元离子单基因函数的参数原理。在孤立的情况下，我们可以使用此工具来证明普遍的OctonionicRouché的定理。作为应用程序，我们设置了Hurwitz Theorem的广义版本，即使对于Clifford分析案例，也是一种新颖性。
In this paper we apply a homologous version of the Cauchy integral formula for octonionic monogenic functions to introduce for this class of functions the notion of multiplicity of zeroes and $a$-points in the sense of the topological mapping degree. As a big novelty we also address the case of zeroes lying on certain classes of compact zero varieties. This case has not even been studied in the associative Clifford analysis setting so far. We also prove an argument principle for octonionic monogenic functions for isolated zeroes and for non-isolated compact zero sets. In the isolated case we can use this tool to prove a generalized octonionic Rouché's theorem by a homotopic argument. As an application we set up a generalized version of Hurwitz theorem which is also a novelty even for the Clifford analysis case.
