论文标题
对频谱参数的非线性依赖性的符号特征值问题的重新归一化振荡理论
Renormalized Oscillation Theory for Symplectic Eigenvalue Problems with Nonlinear Dependence on the Spectral Parameter
论文作者
论文摘要
在本文中，我们建立了针对DIRICHLET边界条件的离散符号特征值问题的新的重新归一化振荡定理。这些定理呈现问题的有限特征值以任意间隔$（a，b）$的数量，该焦点是使用与wronskian相关的转换的相关基础的焦点数量单调性假设在我们的处理中，我们承认符号系统系数中可能的振荡，通过将其非恒定等级相对于频谱参数。
In this paper we establish new renormalized oscillation theorems for discrete symplectic eigenvalue problems with Dirichlet boundary conditions. These theorems present the number of finite eigenvalues of the problem in arbitrary interval $(a,b]$ using number of focal points of a transformed conjoined basis associated with Wronskian of two principal solutions of the symplectic system evaluated at the endpoints $a$ and $b.$ We suppose that the symplectic coefficient matrix of the system depends nonlinearly on the spectral parameter and that it satisfies certain natural monotonicity assumptions. In our treatment we admit possible oscillations in the coefficients of the symplectic system by incorporating their nonconstant rank with respect to the spectral parameter.
