剩余流与主值流乘积的正则化
Regularizations of products of residue and principal value currents
摘要：
我们证明了对应于一对定义完全交的全纯函数的Coleff-Herrera剩余流可以作为自然光滑$(0,2)$ -形式依赖于两个参数的无限制弱极限而得到.此外，我们还证明了该算法的收敛速率是Hölder。这一结果是相反的事实，首先发现的Passare和Tsikh，即剩余积分一般是不连续的起源。我们还将我们的正则化结果推广到所谓的Bochner-Martinelli对，或者更一般地，在完全相交的情况下，Cauchy-Fantappie-Leray块。
英文摘要：
We prove that the Coleff-Herrera residue current, corresponding to a pair of holomorphic functions defining a complete intersection, can be obtained as the unrestricted weak limit of a natural smooth $(0,2)$-form depending on two parameters. Moreover, we prove that the rate of convergence is Hölder. This result is in contrast to the fact, first discovered by Passare and Tsikh, that the residue integral in general is discontinuous at the origin. We also generalize our regularization results to pairs of so called Bochner-Martinelli, or more generally, Cauchy-Fantappie-Leray blocks in the case of a complete intersection.
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