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Finite Sections of Periodic Schrödinger Operators
Publikationstyp
Book Part
Date Issued
2023
Sprache
English
Author(s)
First published in
Number in series
292
Volume
292
Start Page
115
End Page
144
Citation
Operator Theory: Advances and Applications 292: 115-114 (2023)
Publisher DOI
Scopus ID
Publisher
Birkhäuser
ISBN
978-3-031-38020-4
978-3-031-38019-8
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 Hn. 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, λ} -valued potentials with fixed rational λ and period less than nine as well as for arbitrary real-valued potentials of period two.
DDC Class
600: Technology