具有周期势和消失不稳定区间的$\mathbb{R}^2$中的正则系统
Canonical systems in $\mathbb{R}^2$ with periodic potentials and vanishing instability intervals
摘要：
研究了具有绝对连续实对称$π$ -周期势矩阵的$\mathbb{R}^2$中的正则系统.对判别式进行了深入的分析，并对$[0,π]$上的周期、反周期和Dirichlet型边值问题的特征值进行了索引和交织.用Dirichlet型特征值刻画了周期和反周期特征值。证明了所有不稳定区间为零的充要条件是势函数是绝对连续的实值函数与单位矩阵的乘积。
英文摘要：
Canonical systems in $\mathbb{R}^2$ with absolutely continuous real symmetric $π$-periodic potentials matrices are considered. A through analysis of the discriminant is given along with the indexing and interlacing of the eigenvalues of the periodic, anti-periodic and Dirichlet-type boundary value problems on $[0,π]$. The periodic and anti-periodic eigenvalues are characterized in terms of Dirichlet type eigenvalues. It is shown that all instability intervals vanish if and only if the potential is the product of an absolutely continuous real valued function with the identity matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
