On the Classification of Points of a Unit Circle for Subharmonic Functions of the Class $$\mathfrak{A}{\kern 1pt} \text{*}$$

IF 0.5 Q3 MATHEMATICS
S. L. Berberyan
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引用次数: 0

Abstract

A class \(\mathfrak{A}{\kern 1pt} \text{*}\) consisting of subharmonic functions in the unit disk such that their superpositions with some families of linear fractional automorphisms of the disk form normal families is considered. A theorem stating that for any function of class \(\mathfrak{A}{\kern 1pt} \text{*}\) the set of points of the unit circle can be represented as a union of a set of Fatou points, a set of generalized Plesner points, and a set of measure zero is proved.

论$$\mathfrak{A}{/kern 1pt} 类次谐函数单位圆上点的分类\text{*}$$
抽象地考虑了单位圆盘中的次谐函数组成的类(\mathfrak{A}{\kern 1pt} \text{*}),使得它们与圆盘的某些线性分数自变量族的叠加形成正则族。证明了一个定理,即对于任何类 \(\mathfrak{A}\{kern 1pt} \text{*}\)的函数,单位圆的点集都可以表示为法图点集合、广义普莱斯纳点集合和度量为零的集合的联合。
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来源期刊
Russian Mathematics
Russian Mathematics MATHEMATICS-
CiteScore
0.90
自引率
25.00%
发文量
0
期刊介绍: Russian Mathematics  is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.
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