A Matrix-Valued Aleksandrov Disintegration Theorem
A Matrix-Valued Aleksandrov Disintegration Theorem
复制标题
矩阵值 Aleksandrov 衰变定理
DOI：
10.1007/s11785-009-0007-3
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发表时间：
2010
影响因子：
0.8
通讯作者：
Sam Elliott
中科院分区：
文献类型：
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作者：
Sam Elliott
该系统的措施所构建的克拉克（J分析数学25：169-191，1972年），并广泛研究了亚历山德罗夫和其他人提供有用的信息的性质分析自映射的单位光盘。在他们的论文中，Kapustin和Poltoratski（J Funct Anal 238：313-326，2006）扩展了这个概念，以包括算子（以及矩阵）值解析函数，尽管他们将注意力限制在算子值内函数的有趣特殊情况上。在本文中，我们提出了一个替代（虽然等价）的建设，它只适用于矩阵值的情况下，虽然不仅内部功能。这种结构为我们提供了有趣的类似物的某些定理已知是真实的标量的情况下。特别是，我们提出了一个矩阵值推广著名的亚历山德罗夫分解定理（Inv Akad Nauk ArmSSR Mat 22：490-503，1987）的证明，以一定的一类矩阵值的功能。
The system of measures constructed by Clark (J Anal Math 25:169–191, 1972), and studied extensively by Aleksandrov and others provide useful information about the properties of analytic self-maps of the unit disc. In their paper, Kapustin and Poltoratski (J Funct Anal 238:313–326, 2006) extended the concept to include operator (and hence matrix) valued analytic functions, though they restrict their attention to the interesting special case of operator-valued inner functions. In this paper, we present an alternative (though equivalent) construction, which applies only to the matrix-valued case, though not only to inner functions. This construction provides us with interesting analogues of certain theorems known to be true in the scalar case. In particular, we present a proof of a matrix-valued generalisation of the celebrated Aleksandrov Disintegration Theorem (Inv Akad Nauk ArmSSR Mat 22:490–503, 1987) to a certain class of matrix-valued functions.