Lindner, MarkoMarkoLindnerUkena, RikoRikoUkena2022-09-302022-09-302023-06-15Journal of Mathematical Analysis and Applications 522 (2): 126984 (2023-06-15)http://hdl.handle.net/11420/13692We study 1D discrete Schrödinger operators H with integer-valued potential and show that, (i), invertibility (in fact, even just Fredholmness) of H always implies invertibility of its half-line compression H₊ (zero Dirichlet boundary condition, i.e. matrix truncation). In particular, the Dirichlet eigenvalues avoid zero -- and all other integers. We use this result to conclude that, (ii), the finite section method (approximate inversion via finite and growing matrix truncations) is applicable to H as soon as H is invertible. The same holds for H₊.en1096-081320232ElsevierMathematics - Functional AnalysisMathematics - Functional AnalysisComputer Science - Numerical AnalysisMathematics - Numerical AnalysisMathematics - Spectral Theory47N4047B3647B9365J10MathematikJournal Article10.1016/j.jmaa.2022.1269842208.04015v3Journal Article