论文标题
$ n $二维二次圆锥的定期功能较弱
Weak slice regular functions on the $n$-dimensional quadratic cone of octonions
论文作者
论文摘要
在超复杂设置中的切片分析文献中，有两种主要方法可以在一个变量中定义切片的常规函数：一个是要求对任何复杂平面的限制是holomorthic的（具有相同的复杂平面结构），第二种是一种使用茎和切片功能。到目前为止，在几个超复合变量的设置中，仅考虑了第二种方法，即基于stem函数的方法。在本文中，我们将第一个定义用于所谓的$ n $二维二次圆锥体。这两种方法在轴向对称的切片域上产生相同类别的切片常规功能，但是，它们在其他类型的域上是不同的。我们称这类新的功能较弱的切片常规。我们表明，在第二种方法中，存在较弱的定期函数，这些函数在第二种方法中并非固定。此外，我们研究了这些功能的各种特性，包括泰勒扩张。
In the literature on slice analysis in the hypercomplex setting, there are two main approaches to define slice regular functions in one variable: one consists in requiring that the restriction to any complex plane is holomorphic (with the same complex structure of the complex plane), the second one makes use of stem and slice functions. So far, in the setting of several hypercomplex variables, only the second approach has been considered, i.e. the one based on stem functions. In this paper, we use instead the first definition on the so-called $n$-dimensional quadratic cone of octonions. These two approaches yield the same class of slice regular functions on axially symmetric slice-domains, however, they are different on other types of domains. We call this new class of functions weak slice regular. We show that there exist weak slice regular functions which are not slice regular in the second approach. Moreover, we study various properties of these functions, including a Taylor expansion.
