论文标题
Cauchy-Riemann运营商和对实际代数的本地切片分析
Cauchy-Riemann operators and local slice analysis over real alternative algebras
论文作者
论文摘要
我们证明了一些公式与替代 * - 代数的超复合子空间定义的cauchy-riemann运算符与与slice-reformulartity和球形狄拉克运算符概念相关的差分运算符。这些结果尤其允许引入局部切片定期函数的定义，并为局部切片分析打开路径。由于Cauchy-Riemann操作员将相应的Laplacian运算符因素，因此经过验证的公式让我们还获得了有关切片规范函数的谐波和多结性特性的几个结果。
We prove some formulas relating Cauchy-Riemann operators defined on hypercomplex subspaces of an alternative *-algebra to a differential operator associated with the concept of slice-regularity and to the spherical Dirac operator. These results in particular allow to introduce a definition of locally slice-regular function and open the path for local slice analysis. Since Cauchy-Riemann operators factor the corresponding Laplacian operators, the proven formulas let us also obtain several results about the harmonicity and polyharmonicity properties of slice-regular functions.
