多极格林函数的收敛性
Convergence of multipole Green functions
摘要：
在极点碰撞的情况下，我们继续研究了$\mathbb C^n$中有界超凸区域上多极复格林函数的收敛性。我们考虑的情况下，所有的极点不收敛到同一点的区域，其中一些可能会去域的边界。我们证明，弱收敛将意味着收敛的能力，它意味着收敛一致的收敛时，没有极点趋于边界，研究可以减少，在某种意义上说，极点趋于一个单一的点的情况下。证明了格林函数的极限可以作为$\max_{1\le i\le 3n} \frac{1}{p} \log |f_i|$型函数的极限得到，其中$f_i$是全纯函数.
英文摘要：
We continue the study of convergence of multipole pluricomplex Green functions for a bounded hyperconvex domain of $\mathbb C^n$, in the case where poles collide. We consider the case where all poles do not converge to the same point in the domain, and some of them might go to the boundary of the domain. We prove that weak convergence will imply convergence in capacity; that it implies convergence uniformly on compacta away from the poles when no poles tend to the boundary; and that the study can be reduced, in a sense, to the case where poles tend to a single point. Furthermore, we prove that the limits of Green functions can be obtained as limits of functions of the type $\max_{1\le i\le 3n} \frac{1}{p} \log |f_i|$, where the $f_i$ are holomorphic functions.
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