论文标题
在几个变量中的切片中的切片定期函数的表示公式
A representation formula for slice regular functions over slice-cones in several variables
论文作者
论文摘要
本文的目的是将所谓的切片分析扩展到一个普通情况，在该情况下，密码域是均匀维度的真实矢量空间，即$ \ mathbb {r}^{2n} $的形式。我们在$ [end（\ Mathbb {r}^{2n}）]^D $中定义了一个圆锥$ \ mathcal {w} _ \ Mathcal {C}^d $，我们将slice-Topology $τ_s$扩展到该锥体。可以在$ \ left（τ_s，\ Mathcal {w} _ \ Mathcal {C}^d \ right）$中定义切片的常规功能，并且在此框架中可以证明许多结果，其中一个表示公式。该理论可以应用于一些实际代数，称为左切片复杂结构代数。这些代数包括四元组，八元，克利福德代数和真正的替代$*$ - 代数，但还包括左替代代数和镇静，从而在切片分析中提供了全新的环境。
The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form $\mathbb{R}^{2n}$. We define a cone $\mathcal{W}_\mathcal{C}^d$ in $[End(\mathbb{R}^{2n})]^d$ and we extend the slice-topology $τ_s$ to this cone. Slice regular functions can be defined on open sets in $\left(τ_s,\mathcal{W}_\mathcal{C}^d\right)$ and a number of results can be proved in this framework, among which a representation formula. This theory can be applied to some real algebras, called left slice complex structure algebras. These algebras include quaternions, octonions, Clifford algebras and real alternative $*$-algebras but also left-alternative algebras and sedenions, thus providing brand new settings in slice analysis.
