On the theory of matrix-valued functions belonging to the Smirnov class
On the theory of matrix-valued functions belonging to the Smirnov class
复制标题
Smirnov类矩阵值函数理论
DOI：
10.1007/978-3-0348-8944-5_14
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
B. Kirstein
中科院分区：
文献类型：
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作者：
V. Katsnelson;B. Kirstein
本文系统地发展了矩阵Smirnov类的矩阵值函数理论。特别地，V.I. Smirnov，内外因子分解，外函数的Smirnov-Beurling特征和Frostman定理的一个类似物被提出用于Smirnov类的矩阵值函数。我们还考虑了一类属于矩阵Smirnov类的函数族，它是由一个复参数λ索引的。我们证明了，除了一个“非常小”的集合，这样的λ的相应的内因子的内-外因子分解的函数Fλ是一个Blaschke-Potapov积。
A theory of matrix-valued functions from the matricial Smirnov class is systematically developed. In particular, the maximum principle of V.I. Smirnov, inner-outer factorization, the Smirnov-Beurling characterization of outer functions and an analogue of Frostman’s theorem are presented for matrix-valued functions from the Smirnov class. We also consider a family of functions belonging to the matricial Smirnov class which is indexed by a complex parameter λ. We show that with the exception of a “very small” set of such λ the corresponding inner factor in the inner-outer factorization of the function Fλ is a Blaschke-Potapov product.