论文标题
无反射的规范系统，I。AROV仪表和右限制
Reflectionless canonical systems, I. Arov gauge and right limits
论文作者
论文摘要
在频谱理论中，$ j $ - 单调的$ 2 \ times 2 $矩阵函数作为许多一维操作员的传输矩阵出现。从AROV仪表中的规范系统的角度来看，我们提出了此类家庭的一般理论。该系统类似于Schur算法的连续版本，并允许沿Infinity在Infinity相关边界值的流动恢复任意Schur函数。除了在AROV仪表中的结果外，这还提供了对Krein-de Branges公式和无反射特性的无关透视的观点，这些特性在绝对连续的频谱上提供了右界限。这项工作在分解域的内点相对于标准化具有更好行为的逆频谱问题。
In spectral theory, $j$-monotonic families of $2\times 2$ matrix functions appear as transfer matrices of many one-dimensional operators. We present a general theory of such families, in the perspective of canonical systems in Arov gauge. This system resembles a continuum version of the Schur algorithm, and allows to restore an arbitrary Schur function along the flow of associated boundary values at infinity. In addition to results in Arov gauge, this provides a gauge-independent perspective on the Krein-de Branges formula and the reflectionless property of right limits on the absolutely continuous spectrum. This work has applications to inverse spectral problems which have better behavior with respect to a normalization at an internal point of the resolvent domain.
