论文标题
规范系统的单片矩阵的增长估计值
A growth estimate for the monodromy matrix of a canonical system
论文作者
论文摘要
我们研究了极限圆圈中的二维规范系统的光谱。它是离散的，并且通过克雷因·戴·布兰格斯公式，不能比整数更密集。但是在许多情况下，它会更稀疏。特定的自我偶像实现的频谱与系统单构矩阵的一个条目的零相吻合。因此，经典函数理论建立了单构基质的生长与光谱的分布之间的直接联系。我们证明了单型矩阵的通用和挠性上限估计值，使用它证明了连续的哈密顿量的结合，并构造了示例，这些示例表明该结合是锋利的。前两个结果沿R.Romanov早期工作的线条进行，但在这些结果上显着改善。即使是在指数级的粗略规模上也可以看到这一点。
We investigate the spectrum of 2-dimensional canonical systems in the limit circle case. It is discrete and, by the Krein-de Branges formula, cannot be more dense than the integers. But in many cases it will be more sparse. The spectrum of a particular selfadjoint realisation coincides with the zeroes of one entry of the monodromy matrix of the system. Classical function theory thus establishes an immediate connection between the growth of the monodromy matrix and the distribution of the spectrum. We prove a generic and flexibel upper estimate for the monodromy matrix, use it to prove a bound for the case of a continuous Hamiltonian, and construct examples which show that this bound is sharp. The first two results run along the lines of earlier work of R.Romanov, but significantly improve upon these results. This is seen even on the rough scale of exponential order.
