Boundary convergence of vector-valued pseudocontinuable functions☆
Boundary convergence of vector-valued pseudocontinuable functions☆
复制标题
向量值伪连续函数的边界收敛☆
DOI：
10.1016/j.jfa.2006.04.006
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发表时间：
2006
影响因子：
1.7
通讯作者：
A. Poltoratski
中科院分区：
文献类型：
--
作者：
V. Kapustin;A. Poltoratski
在本文的第一部分，我们讨论了D. Clark著名构造的多维模拟，它允许人们研究模型收缩扰动的谱测度族。第二部分对拟可连续函数的边界行为的有关结果进行了推广。我们证明，尽管关于伪连续函数关于Clark测度边值存在性的标量定理的最直接类比在非标量情况下是失败的，但是我们可以找到合适的向量值版本。
In the first part of the paper we discuss a multi-dimensional analogue of the well-known construction by D. Clark that allows one to study families of spectral measures of perturbations of the model contraction. In the second part we present extensions of the relevant results on the boundary behavior of pseudocontinuable functions. We show that, although the most direct analogue of the scalar theorem on the existence of boundary values for pseudocontinuable functions with respect to Clark measures fails in the non-scalar situation, suitable vector-valued versions of such results can be found.