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  4. Finite Sections of Periodic Schrödinger Operators
 
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Finite Sections of Periodic Schrödinger Operators

Publikationstyp
Book Part
Date Issued
2023
Sprache
English
Author(s)
Gabel, Fabian 
Mathematik E-10  
Gallaun, Dennis  orcid-logo
Mathematik E-10  
Großmann, Julian  orcid-logo
Lindner, Marko  orcid-logo
Mathematik E-10  
Ukena, Riko  orcid-logo
Mathematik E-10  
TORE-URI
https://hdl.handle.net/11420/45281
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
10.1007/978-3-031-38020-4_6
Scopus ID
2-s2.0-85179702712
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.
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