利用一类Sturmian时间尺度上的线性哈密顿系统统一离散和连续Weyl-Titchmarsh理论
Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales
摘要：
在本研究中，我们考虑Sturmian时间尺度上半直线上一类动态线性Hamilton nabla系统的Weyl-Titchmarsh理论.在发展了解的基本性质和正则谱问题之后，我们引入了系统相应的极大和极小算子。构造了矩阵圆盘，证明了它是嵌套的，并收敛于一个极限集。建立了极限集的矩阵半径的秩、线性无关平方可和解的个数与极小算子的亏指数之间的精确关系。利用上述结果，根据极小算子的亏损指数对奇异动态线性Hamilton nabla系统进行了分类，并分别得到了系统在极限点和极限圆情形下的几个等价条件.这些结果统一和扩展某些经典和最近的结果在连续和离散的情况下，分别对Sturmian时间尺度的主题。
英文摘要：
In this study, we are concerned with introducing Weyl-Titchmarsh theory for a class of dynamic linear Hamiltonian nabla systems over a half-line on Sturmian time scales. After developing fundamental properties of solutions and regular spectral problems, we introduce the corresponding maximal and minimal operators for the system. Matrix disks are constructed and proved to be nested and converge to a limiting set. Some precise relationships among the rank of the matrix radius of the limiting set, the number of linearly independent square summable solutions, and the defect indices of the minimal operator are established. Using the above results, a classification of singular dynamic linear Hamiltonian nabla systems is given in terms of the defect indices of the minimal operator, and several equivalent conditions on the cases of limit point and limit circle are obtained, respectively. These results unify and extend certain classic and recent results on the subject in the continuous and discrete cases, respectively, to Sturmian time scales.
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。
