Oszillations- und Spektraltheorie von Differenzial- und Differenzengleichungssystemen

该项目的目的是研究线性哈密顿微分系统和辛差分系统的解的定性行为。将研究以下特定主题：线性Hamilton微分系统的定性理论，不假设可控性（相同的正规性）辛差分系统的Sturmian理论辛差分系统的旋转数与Hamilton和辛系统相关的算子的谱理论带状对称矩阵，差分算子及其谱的数值分析

The aim of the project is to study the qualitative behaviour of solutions of linear Hamiltonian differential systems and of symplectic difference systems. The following particular subjects will be studied: Qualitative theory of linear Hamiltonian differential systems without the assumption of controllability (identical normality) Sturmian theory for symplectic difference systems Rotation numbers for symplectic difference systems Spectral theory of operators associated with Hamiltonian and symplectic systems Banded symmetric matrices, difference operators and numerical analysis of their spectrum