The k-Cauchy–Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k-regular functions
The k-Cauchy–Fueter complex, Penrose transformation and Hartogs phenomenon for quaternionic k-regular functions
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DOI：
10.1016/j.geomphys.2009.11.011
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发表时间：
2010-03
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
利用与Penrose变换相关的复几何方法，给出了C4n上一个精确序列的完整推导，该序列在hnn上的相关微分复形是k- cauchy - fueter复形，其第一算子D0(k)湮灭了k-正则函数。D0(1)是通常的Cauchy-Fueter算子，1-正则函数是四元数正则函数。我们还证明了k-Cauchy-Fueter复合体是椭圆形的。利用与k-Cauchy-Fueter复形相关的4阶拉普拉斯算子的基本解，我们可以建立相应的Bochner-Martinelli积分表示公式，求解非齐次k-Cauchy-Fueter方程，并证明k-正则函数在任意有界域上的Hartogs扩展现象。
By using complex geometric method associated to the Penrose transformation, we give a complete derivation of an exact sequence over C4n, whose associated differential complex over Hnis the k-Cauchy–Fueter complex with the first operator D0(k)annihilating k-regular functions. D0(1)is the usual Cauchy–Fueter operator and 1-regular functions are quaternionic regular functions. We also show that the k-Cauchy–Fueter complex is elliptic. By using the fundamental solutions to the Laplacian operators of 4-order associated to the k-Cauchy–Fueter complex, we can establish the corresponding Bochner–Martinelli integral representation formula, solve the non-homogeneous k-Cauchy–Fueter equations and prove the Hartogs extension phenomenon for k-regular functions in any bounded domain.