Options
Finite Sections of Periodic Schrödinger Operators
Publikationstyp
Book Part
Date Issued
2023
Sprache
English
Author(s)
Volume
292
Start Page
115
End Page
144
Citation
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. (2023)
Publisher DOI
Scopus ID
ISSN
02550156
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.