论文标题
零形函数的零子集的必要条件
Necessary and sufficient conditions for zero subsets of holomorphic functions
论文作者
论文摘要
让$ d $是复杂平面中的一个域，$ m $是$ d $的扩展实际功能。如果$ f $是$ d $上的非零全体形状功能，则具有上限$ | f | f | \ leq \ exp m $在此域$ d $上，那么自然可以预期，该功能$ m $ $ m $和domain $ d $ doply holomorphic函数的零的零分布必须有一些限制。我们已经在以前的工作中详细调查了这个问题，当时$ m $是次谐波功能，而域$ d $是任意的或具有非极性边界的情况。答案是通过限制$ f $从上方的零函数的零次函数$ m $ riesz度量的分布来给出的。在本文中，功能$ m $是次谐波函数的差异或$δ$ -Subharmonic函数，并且根据此$δ$ -Subharmonic函数$ M $的RIESZ充电来给出上限。这些结果在一定程度上是次谐波功能$ m $的新事物。域D是复杂平面时的情况。对于复杂平面，可以达到标准水平。
Let $D$ be a domain in the complex plane, $M$ be an extended real function on $D$. If $f$ is a non-zero holomorphic function on $D$ with an upper constraint $|f|\leq \exp M$ on this domain $D$, then it is natural to expect that there must be some upper constraints on the distribution of zeros of this holomorphic function exclusively in terms of the function $M$ and the geometry of the domain $D$. We have investigated this question in detail in our previous works in the case when $M$ is a subharmonic function and the domain $D$ is arbitrary or with a non-polar boundary. The answer was given in terms of limiting the distribution of zeros of $f$ from above via the Riesz measure of the subharmonic function $M$. In this article, the function $M$ is the difference of subharmonic functions, or a $δ$-subharmonic function, and the upper constraints are given in terms of the Riesz charge of this $δ$-subharmonic function $M$. These results are also new to a certain extent for the subharmonic function $M$. The case when the domain D is the complex plane is considered separately. For the complex plane, it is possible to reach the criterion level.
