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A characterization of one‐component inner functions
Bulletin of the London Mathematical Society ( IF 0.9 ) Pub Date : 2020-07-27 , DOI: 10.1112/blms.12395 Artur Nicolau 1 , Atte Reijonen 2
Bulletin of the London Mathematical Society ( IF 0.9 ) Pub Date : 2020-07-27 , DOI: 10.1112/blms.12395 Artur Nicolau 1 , Atte Reijonen 2
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We present a characterization of one‐component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by Cima and Mortini. In particular, we prove that for any inner function whose singular set has measure zero, one can find a Blaschke product such that is one‐component. We also obtain a characterization of one‐component singular inner functions which is used to produce examples of discrete and continuous one‐component singular inner functions.
中文翻译:
单成分内部功能的表征
我们根据其零点的位置及其相关的奇异测度来描述一分量内部函数。结果,我们回答了Cima和Mortini提出的几个问题。特别是,我们证明对于任何内部函数 其奇异集的度量为零,则可以找到一个Blaschke乘积 这样 是一个组成部分。我们还获得了单成分奇异内部函数的表征,该特性用于生成离散和连续的单成分奇异内部函数的示例。
更新日期:2020-07-27
中文翻译:
单成分内部功能的表征
我们根据其零点的位置及其相关的奇异测度来描述一分量内部函数。结果,我们回答了Cima和Mortini提出的几个问题。特别是,我们证明对于任何内部函数 其奇异集的度量为零,则可以找到一个Blaschke乘积 这样 是一个组成部分。我们还获得了单成分奇异内部函数的表征,该特性用于生成离散和连续的单成分奇异内部函数的示例。