论文标题
逆频谱问题的ETUDES
Etudes for the inverse spectral problem
论文作者
论文摘要
在本说明中，我们研究了典型的哈密顿系统的逆频谱问题，该系统涵盖了一半的二阶微分方程。我们的目标是将Marchenko，Gelfand-Levitan和Kerin的工作中开发的经典结果扩展到更广泛的规范系统，并用各种示例说明解决方案算法和公式。我们方法的主要成分之一是使用截短的Toeplitz运算符，它补充了Krein-de Branges规范系统理论的标准工具箱。
In this note we study inverse spectral problems for canonical Hamiltonian systems, which encompass a broad class of second order differential equations on a half-line. Our goal is to extend the classical resultss developed in the work of Marchenko, Gelfand-Levitan, and Krein to broader classes of canonical systems and to illustrate the solution algorithms and formulas with a variety of examples. One of the main ingredients of our approach is the use of truncated Toeplitz operators, which complement the standard toolbox of the Krein-de Branges theory of canonical systems.
