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Regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. (English) Zbl 1380.39010

Summary: This paper is concerned with regular approximations of spectra of singular discrete linear Hamiltonian systems with one singular endpoint. For any given self-adjoint subspace extension (SSE) of the corresponding minimal subspace, its spectrum can be approximated by eigenvalues of a sequence of induced regular SSEs, generated by the same difference expression on smaller finite intervals. It is shown that every SSE of the minimal subspace has a pure discrete spectrum, and the \(k\)-th eigenvalue of any given SSE is exactly the limit of the \(k\)-th eigenvalues of the induced regular SSEs; that is, spectral exactness holds, in the limit circle case. Furthermore, error estimates for the approximations of eigenvalues are given in this case. In addition, in the limit point and intermediate cases, spectral inclusive holds.

MSC:

39A12 Discrete version of topics in analysis
39A10 Additive difference equations
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
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