The main result of the paper is a criterion for a sequence of points in a domain of the complex plane, giving necessary and sufficient conditions under which this sequence of points is an exact sequence of zeros of some holomorphic function whose logarithm of modulus is majored by a given subharmonic function in the domain under consideration. Our criterion for the distribution of zeros of holomorphic functions with a given majorant is formulated in terms of special integral estimates and uses a new notion we recently introduced of affine balayage of measures. In one of our previous joint communications this criterion was announced without any proof. Here we fill this gap and give a criterion with exact definitions and a complete proof.

中文翻译：

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全纯函数根序列的准则及其生长限制

本文的主要结果是在复平面的一个域中确定点序列的准则，给出了必要和充分的条件，在该条件下，该点序列是某些全纯函数的零的精确序列，其模数的对数主要为在考虑的域中给定的次谐波函数。我们用给定的主要变量的全纯函数零点分布的标准是根据特殊的积分估计制定的，并使用了我们最近引入的度量仿射方法的新概念。在我们之前的一次联合通讯中，此标准未经任何宣布就宣布了。在这里，我们填补了这一空白，并给出了具有确切定义和完整证明的标准。