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Discrete linear Hamiltonian eigenvalue problems. (English) Zbl 0933.39033
Summary: This paper introduces general discrete linear Hamiltonian eigenvalue problems and characterizes the eigenvalues. Assumptions are given, among them the new notion of strict controllability of a discrete system, that imply isolatedness and lower boundedness of the eigenvalues. Due to the quite general assumptions, discrete Sturm-Liouville eigenvalue problems of higher order are included in the presented theory.
MSC:
39A12Discrete version of topics in analysis
93B05Controllability
34L15Eigenvalues, estimation of eigenvalues, upper and lower bounds for OD operators
34B24Sturm-Liouville theory