论文标题
几个Quaternionic变量功能的Wintinger运算符
Wirtinger operators for functions of several quaternionic variables
论文作者
论文摘要
我们介绍了几个四离子变量功能的Wirtinger运算符。这些运算符是真正的线性偏差算子，在Quaternionic多项式上表现良好，具有类似于几个复杂变量的Wirewtinger衍生物所满足的属性。由于变量的非交换性，直线运算符被证明是更高级别的，除了第一阶的第一个阶层。尽管如此，这些操作员互相通勤并满足了产品的莱布尼兹规则。此外，它们表征了切片规则多项式的类别，更普遍地是切片的Quaternionic函数。作为迈向Wirtinger运算符的定义的一步，我们为切片函数和几个变量的切片函数提供了almansi-Type分解。我们还基于$ n $二维Quaternionic Space的任何开放子集的局部切片规范功能的定义，介绍了本地切片分析的某些方面。
We introduce Wirtinger operators for functions of several quaternionic variables. These operators are real linear partial differential operators which behave well on quaternionic polynomials, with properties analogous to the ones satisfied by the Wirtinger derivatives of several complex variables. Due to the non-commutativity of the variables, Wirtinger operators turn out to be of higher order, except the first ones that are of the first order. In spite of that, these operators commute each other and satisfy a Leibniz rule for products. Moreover, they characterize the class of slice-regular polynomials, and more generally of slice-regular quaternionic functions. As a step towards the definition of the Wirtinger operators, we provide Almansi-type decompositions for slice functions and for slice-regular functions of several variables. We also introduce some aspects of local slice analysis, based on the definition of locally slice-regular function in any open subset of the $n$-dimensional quaternionic space.
