权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

The Algebras of Bounded Analytic Functions on a Riemann Surface and the isomorphic problem

黎曼曲面上有界解析函数的代数与同构问题

基本信息

批准号：
12640147
负责人：
HAYASHI Mikihiro
金额：
$ 2.56万
依托单位：
HOKKAIDO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640147/
关键词：
Rieman surface bounded analytic function maximal ideal space point separation problem isomorphic problem Hardy class Myrberg phenomena uniqueness theorem 葉被覆面有界正則関数環 Hardy族 Myrberg現象 2葉被覆面

项目摘要

The algebra of all bounded analytic functions on a Riemann surface is of course determined by the Riemann surface. This converse is no longer obvious, and we call it the isomorphic problem. If a Riemann surface admits a meromorphic function bounded at the boundary of the surface and if bounded analytic functions separate the points of the surface, then the answer is yes. However, the investigator found a counter example when a surface admits no such meromorphic function.When we ask the isomorphic problem, we assume that bounded analytic functions (weakly) separate the points of a surface, for otherwise isomorphic problem fails always. Thus, it is an interesting problem to determine whether a given surface is separating or not with respect to bounded analytic functions. This problem is also hard to solve in general. The investigator, together with Prof. Mitsuru Nakai and Dc. Yasuyuki Kobayashi, consider the case of a two-sheeted disc, where the projection of the sequence of ramification points converging to the center of the disc. We considered the case that a sequence of small discs centered at ramification points are removed, and found several sufficient conditions for separating and also not separating.

黎曼曲面上所有有界解析函数的代数当然由黎曼曲面决定。这个逆命题不再明显，我们称之为同构问题。如果黎曼曲面允许亚纯函数在曲面边界处有界，并且有界解析函数将曲面的点分开，那么答案是肯定的。然而，研究人员发现了一个反例，当一个表面不承认这样的亚纯函数时。当我们问同构问题时，我们假设有界解析函数（弱地）分离表面的点，否则同构问题总是失败。因此，确定给定表面相对于有界解析函数是否分离是一个有趣的问题。这个问题一般来说也很难解决。研究人员与 Mitsuru Nakai 教授和 Dc. Yasuyuki Kobayashi，考虑两片圆盘的情况，其中分支点序列的投影会聚到圆盘的中心。我们考虑了以分枝点为中心的一系列小圆盘被移除的情况，并找到了几个分离和不分离的充分条件。