论文标题
almansi-Type分解，用于几个Quaternionic变量的定期函数
Almansi-type decomposition for slice regular functions of several quaternionic variables
论文作者
论文摘要
在本文中，我们提出了一个almansi-type分解，以用于几个四离子变量的定期函数。我们的方法在$ \ mathbb {h}^n $中的任何切片函数中产生$ 2^n $不同的分解。根据分解的选择，每个组件都被明确，唯一确定并具有理想的特性，例如所选变量中的谐波和循环。作为这些分解的后果，我们在$ \ mathbb {h}^n $中提供了另一个证明Fueter定理的证明，在每个变量中建立了slice常规函数的双重性，并为其提供平均值和Poisson公式。
In this paper we propose an Almansi-type decomposition for slice regular functions of several quaternionic variables. Our method yields $2^n$ distinct and unique decompositions for any slice function with domain in $\mathbb{H}^n$. Depending on the choice of the decomposition, every component is given explicitly, uniquely determined and exhibits desirable properties, such as harmonicity and circularity in the selected variables. As consequences of these decompositions, we give another proof of Fueter's Theorem in $\mathbb{H}^n$, establish the biharmonicity of slice regular functions in every variable and derive mean value and Poisson formulas for them.
