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Defect indices and definiteness conditions for a class of discrete linear Hamiltonian systems. (English) Zbl 1256.39004

Authors’ abstract: This paper is concerned with a class of discrete linear Hamiltonian systems in finite or infinite intervals. A definiteness condition and its equivalent statements are discussed and three sufficient conditions for the definiteness condition are given. A precise relationship between the defect index of the minimal subspace generated by the system and the number of linearly independent square summable solutions of the system is established. In particular, they are equal if and only if the definiteness condition is satisfied. Finally, two criteria for the limit point case and one criterion for the limit circle case are obtained.

MSC:

39A12 Discrete version of topics in analysis
39A06 Linear difference equations
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
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