论文标题
一个成分内部函数的表征
A Characterization of One-component Inner Functions
论文作者
论文摘要
我们介绍了单组分内函数的表征，其零的位置及其相关的单数度度量。结果，我们回答了J. Cima和R. Mortini提出的几个问题。特别是，我们证明，对于任何内部功能$θ$的单数套件的测量零，可以找到blaschke product $ b $，因此$θb$是一个组件。我们还获得了一个成分单数内部函数的表征，该功能用于产生离散和连续的单组分奇异内部函数的示例。
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 J. Cima and R. Mortini. In particular we prove that for any inner function $Θ$ whose singular set has measure zero, one can find a Blaschke product $B$ such that $ΘB$ 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.
