论文标题
几何函数理论超过Quaternionic Slice域
Geometric function theory over quaternionic slice domains
论文作者
论文摘要
2006年推出了四个离子切片的常规功能理论，并在对称切片域上成功开发了大约十年，这似乎是他们研究的自然环境。最近的一些文章为该理论的进一步发展铺平了道路：即，对不一定是对称的切片域上进行了定期功能的研究。目前的工作是在新现象出现的新情况下的几何函数理论的全景。例如，零集的性质可能与在对称情况下大不相同。这项工作包括差分，代数，拓扑特性，以及在切片域上的定期函数的积分和串联表示。
The theory of quaternionic slice regular functions was introduced in 2006 and successfully developed for about a decade over symmetric slice domains, which appeared to be the natural setting for their study. Some recent articles paved the way for a further development of the theory: namely, the study of slice regular functions on slice domains that are not necessarily symmetric. The present work is a panorama of geometric function theory in this new context, where new phenomena appear. For instance, the nature of the zero sets can be drastically different than in the symmetric case. The work includes differential, algebraic, topological properties, as well as integral and series representations, of slice regular functions over slice domains.
