基于Maslov指标的[0，1]上线性哈密顿系统的重整化振动理论
Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index
摘要：
工作与一般类的线性哈密顿系统$[0, 1]$，我们表明，重整化振荡的结果可以得到一个自然的方式，通过考虑适当选择路径的拉格朗日子空间的$\mathbb{C}^{2n}$的Maslov指数。我们验证，我们的适用性类包括狄拉克和Sturm-Liouville系统，以及系统所产生的微分-代数方程的谱参数出现非线性。
英文摘要：
Working with a general class of linear Hamiltonian systems on $[0, 1]$, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropriately chosen paths of Lagrangian subspaces of $\mathbb{C}^{2n}$. We verify that our applicability class includes Dirac and Sturm-Liouville systems, as well as a system arising from differential-algebraic equations for which the spectral parameter appears nonlinearly.
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