Conditions, including criteria, are established for the existence of a continuous linear right inverse to a surjective convolution operator in the space of germs of analytic functions on a convex subset of the complex plane which has a countable neighbourhood basis consisting of convex domains. These are stated in terms of the existence of special families of subharmonic functions and the boundary behaviour of convex conformal mappings related to the sets in question. Bibliography: 50 titles.

中文翻译：

---

边界上有开放障碍的复平面上凸集上的卷积方程的解析解

建立条件，包括判据，为在复数平面的凸子集上的解析函数的菌群空间中存在与射影卷积算子相反的连续线性右逆的存在，该复平面的凸子集具有由凸域组成的可数邻域。这些是根据亚谐波函数的特殊族的存在以及与所讨论的集合有关的凸共形映射的边界行为来陈述的。参考书目：50种。