单分量内函数的一个特征
A Characterization of One-component Inner Functions
摘要：
我们提出了一个特征的单分量内函数在其零点的位置和相关的奇异测度。因此，我们回答了J.Cima和R.莫蒂尼特别是，我们证明了任何内部功能$Θ$的奇异集的措施为零，可以找到一个Blaschke产品$B$，使$ΘB$是一个组件。我们还得到了一个特征的单组分奇异内函数，这是用来产生离散和连续的单组分奇异内函数的例子。
英文摘要：
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.
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