Abstract
We study discrete Schrödinger operators H with periodic potentials as they are typically used to approximate aperiodic Schrödinger operators like the Fibonacci Hamiltonian. We prove an efficient test for applicability of the finite section method, a procedure that approximates H by growing finite square submatrices \(H_n\). For integer-valued potentials, we show that the finite section method is applicable as soon as H is invertible. This statement remains true for \(\{0,\lambda \}\)-valued potentials with fixed rational \(\lambda \) and period less than nine as well as for arbitrary real-valued potentials of period two.
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The authors would like to thank the anonymous referee for his or her interest and helpful comments on our manuscript.
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Gabel, F., Gallaun, D., Großmann, J., Lindner, M., Ukena, R. (2023). Finite Sections of Periodic Schrödinger Operators. In: Choi, Y., Daws, M., Blower, G. (eds) Operators, Semigroups, Algebras and Function Theory. IWOTA 2021. Operator Theory: Advances and Applications, vol 292. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-38020-4_6
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DOI: https://doi.org/10.1007/978-3-031-38020-4_6
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