论文标题
在与矩阵字符串方程相对应的一类规范系统中
On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory
论文作者
论文摘要
使用特定类别的Volterra运算符与平方集成的一类线性相似性，建立了与基质字符串方程相对应的规范系统的通用基本解决方案的重要表示。这些规范系统的显式基本解决方案也是通过GBDT版本的Darboux变换构建的。给出了动态规范系统的示例和应用。也构建了动态规范系统的明确解决方案。三个附录专用于针对规范系统的Weyl-titchmarsh理论，将规范系统的子类转换为矩阵字符串方程（以及较小的规范系统子类向矩阵Schrödinger方程）以及Volterra操作员的线性相似性问题。
An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared integration. Explicit fundamental solutions of these canonical systems are also constructed via the GBDT version of Darboux transformation. Examples and applications to dynamical canonical systems are given. Explicit solutions of the dynamical canonical systems are constructed as well. Three appendices are dedicated to the Weyl--Titchmarsh theory for canonical systems, transformation of a subclass of canonical systems into matrix string equations (and of a smaller subclass of canonical systems into matrix Schrödinger equations), and a linear similarity problem for Volterra operators.
