We study certain transformations of Nevanlinna families and Schur class operator-valued functions, construct their realizations by means of compressed resolvents and by the transfer functions of conservative systems, and find fixed points of such transformations. In particular, we characterize some automorphic Schur functions and corresponding them Nevanlinna families, including periodic and scale invariant.

中文翻译：

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压缩溶剂，Schur函数，Nevanlinna系列及其转换

我们研究了Nevanlinna族和Schur类算子值函数的某些变换，利用压缩的解析子和保守系统的传递函数来构造它们的实现，并找到这些变换的固定点。特别是，我们刻画了一些自守的Schur函数，并将它们对应于Nevanlinna族，包括周期和尺度不变性。