论文标题
Quaternionic Slice常规功能的局部表示公式
A local representation formula for quaternionic slice regular functions
论文作者
论文摘要
在2006年引入后，Quaternionic Slice常规功能主要是在相对于真实轴对称的域中研究的。这种选择是由2009年发表的一些基本结果激励的，例如轴向对称域的表示公式。 本工作研究将不轴向对称的域的定期功能切开，部分纠正了一些先前发表的结果的假设。特别是，这项工作包括一个无效的局部表示公式，而无需对称假设。此外，它决定了一类称为简单的域类别，具有以下属性：简单域上的每个切片常规函数都可以唯一地扩展到其域的对称完成。
After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as the Representation Formula for axially symmetric domains. The present work studies slice regular functions over domains that are not axially symmetric, partly correcting the hypotheses of some previously published results. In particular, this work includes a Local Representation Formula valid without the symmetry hypothesis. Moreover, it determines a class of domains, called simple, having the following property: every slice regular function on a simple domain can be uniquely extended to the symmetric completion of its domain.
