We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.

我们讨论了可以从“边界测量”中检测到多少有关Friedrichs模型算子的信息（乘积的算子的有限秩扰动）。边界三元组的框架用于引入广义的Titchmarsh–Weyl M函数和可检测子空间，这些子空间与“可从边界测量中访问”的算子部分相关。在本文中，我们选择某些Hardy类中Friedrichs模型中出现的函数作为参数。这使我们能够通过使用相关Toeplitz算符符号的规范Riesz-Nevanlinna分解来确定可检测子空间。