On non-homogeneous Cauchy–Fueter equations and Hartogs’ phenomenon in several quaternionic variables
On non-homogeneous Cauchy–Fueter equations and Hartogs’ phenomenon in several quaternionic variables
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DOI：
10.1016/j.geomphys.2008.04.004
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发表时间：
2008-09
影响因子：
1.5
通讯作者：
Wei Wang
中科院分区：
文献类型：
--
作者：
Wei Wang
柯西-富埃特复形是多个四元数变量理论中Dolbeault复形的对应物。利用H_n上与该微分复形相关的四阶Laplacian算子的基本解，我们可以求解非齐次Cauchy-Fueter方程组，并证明了任意区域上四元数正则函数的Hartogs延拓现象.给出了H值函数的Bochner-Martinelli积分表示公式的四元数形式。
The Cauchy–Fueter complex is the counterpart of the Dolbeault complex in the theory of several quaternionic variables. By using the fundamental solution to the Laplacian operators of fourth order associated to this differential complex on Hn, we can solve the system of non-homogeneous Cauchy–Fueter equations and prove the Hartogs’ extension phenomenon for quaternionic regular functions on any domain. The quaternionic version of Bochner–Martinelli integral representation formula for H-valued functions is also given.