Oszillations- und Spektraltheorie von Differenzial- und Differenzengleichungssystemen

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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