Boundary regularity of Nevanlinna domains and univalent functions in model subspaces
Boundary regularity of Nevanlinna domains and univalent functions in model subspaces
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Nevanlinna域的边界正则性和模型子空间中的单价函数
DOI：
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发表时间：
2011
期刊：
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通讯作者：
K. Fedorovskiy
中科院分区：
文献类型：
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作者：
A. Baranov;K. Fedorovskiy
本文研究了多解析多项式一致逼近问题中出现的Nevanlinna域的边界正则性。本文提出了一种新的构造Nevanlinna域的方法，该域具有基本上不规则的非解析边界，该方法基于在模型子空间中找到合适的单叶函数，即在形式为的子空间中，其中是一个内部函数。为了描述所得到的域的边界的不规则性，使用了Dolzhenko关于共形映射的边界正则性的最近结果。书目：18种。
In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains with essentially irregular nonanalytic boundaries is suggested; this method is based on finding appropriate univalent functions in model subspaces, that is, in subspaces of the form , where is an inner function. To describe the irregularity of the boundaries of the domains obtained, recent results by Dolzhenko about boundary regularity of conformal mappings are used. Bibliography: 18 titles.