Bounded analytic functions on a class of open Riemann surfaces.
Bounded analytic functions on a class of open Riemann surfaces.
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一类开黎曼曲面上的有界解析函数。
DOI：
10.2140/pjm.1975.59.557
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发表时间：
1975
影响因子：
0.6
通讯作者：
Charles Stanton
中科院分区：
文献类型：
--
作者：
Charles Stanton
本文证明了开黎曼曲面的一些函数论性质与有限黎曼曲面穷尽的一个条件有关。引入了一类Myrberg曲面，它们是单位圆盘上的某些分支覆盖曲面。穷尽条件被用来区分有界解析函数在其上分隔点的Myrberg曲面。给出了Myrberg曲面上有界解析函数空间的退化方法的完整描述。穷尽条件用格林函数表示，已知它等价于曲面基本群上的函数论条件。后一个条件表明，该曲面是其有界解析函数的Banach代数的谱的开子集。
In this paper some function theoretic properties of an open Riemann surface are related to a condition on the exhaustion of the surface by finite Riemann surfaces. The class of Myrberg surfaces is introduced; these are certain branched covering surfaces of the unit disc. The exhaustion condition is used to distinguish those Myrberg surfaces on which the bounded analytic functions separate points. A complete description is given of the ways in which the space of bounded analytic functions on a Myrberg surface can de-generate. The exhaustion condition is stated in terms of the Green's function; it is already known to be equivalent to a function theoretic condition on the fundamental group of the surface. This latter condition is shown to imply that the surface is an open subset of the spectrum of its Banach algebra of bounded analytic functions.