Title: The boundary control approach to inverse spectral theory Show Chinese title

Title: 反谱理论的边界控制方法

Abstract: We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed by Remling and the Boundary Control method. We show that the Boundary Control approach provides simple and physically motivated proofs of the central results of other theories. We demonstrate also the connections between the dynamical and spectral data and derive the local version of the classical Gelfand--Levitan equations. Show Chinese abstract

Abstract: 我们建立了逆谱问题的不同方法之间的联系：经典的Gelfand--Levitan理论、Krein方法、Simon理论、Remling提出的方法以及边界控制方法。 我们证明了边界控制方法为其他理论的核心结果提供了简单且有物理意义的证明。 我们还展示了动力学数据与谱数据之间的联系，并推导出经典Gelfand--Levitan方程的局部版本。