论文标题
衡量标准和分布Riesz的仿射量
Affine Balayage of Measures and Distribution of Riesz Measures of Subharmonic Functions
论文作者
论文摘要
我们发展并使用一些潜在理论的关键概念，例如衡量标准及其潜力之间的二元性，以研究亚谐波功能的质量分布，同时限制其在其定义领域的边界附近的生长。它们是根据riesz量度的次谐波功能来制定和证明的。在本文中，对全体形态功能的应用涉及其零集的分布在对该功能增长的限制下。我们文章的辅助结果也可能具有独立的兴趣。首先，这是1）定理粘合谐波函数和使用Green功能粘合下谐波功能的定理； 2）内部描述措施及其潜力之间的双重性； 3）一方面的詹森和阿伦斯·斯宾格的二元性以及另一只手的詹森和阿伦斯·索恩电位； 4）连接亚谐波函数，其Riesz措施，谐波测量和Green功能的经典泊松 - 詹森公式的概括。
We develop and use some key concepts of potential theory, such as balayage and duality between measures and their potentials, to study the distribution of masses of subharmonic functions while restrictions to their growth near the boundary of their domain of definition. They are formulated and proved in terms of the Riesz measure for a subharmonic function. In this article, applications to holomorphic functions concern the distribution of their zero sets under restrictions to growth of this functions. Auxiliary results of our article may also be of independent interest. This is, first of all, 1) theorems on gluing of subharmonic functions and on gluing a subharmonic function with Green's function; 2) an internal description of the duality between balayage of measures and their potentials; 3) the duality between the Jensen and Arens-Singer measures on the one hand and the Jensen and Arens-Singer potentials of on the other; 4) a generalization of classical Poisson-Jensen formula connecting subharmonic functions, their Riesz measures, harmonic measures, and Green's functions.
