Finite section method for aperiodic Schrödinger operators

Publikationstyp
Preprint
Publikationsdatum
2021-04-01
Sprache
English
Author
Gabel, Fabian Nuraddin Alexander 
Gallaun, Dennis orcid-logo
Großmann, Julian Peter orcid-logo
Lindner, Marko orcid-logo
Ukena, Riko orcid-logo
Institut
Mathematik E-10 
TORE-URI
http://hdl.handle.net/11420/13414
Citation
arXiv: 2104.00711 (2021)
Publisher DOI
10.48550/arXiv.2104.00711
ArXiv ID
2104.00711v2
We consider discrete Schrödinger operators with aperiodic potentials given by a Sturmian word, which is a natural generalisation of the Fibonacci Hamiltonian. We introduce the finite section method, which is often used to solve operator equations approximately, and apply it first to periodic Schrödinger operators. It turns out that the applicability of the method is always guaranteed for integer-valued potentials provided that the operator is invertible. By using periodic approximations, we find a necessary and sufficient condition for the applicability of the finite section method for aperiodic Schrödinger operators and a numerical method to check it.
Schlagworte
Mathematics - Spectral Theory
Mathematics - Spectral Theory
Computer Science - Numerical Analysis
Mathematical Physics
Mathematics - Mathematical Physics
Mathematics - Numerical Analysis
65J10, 47B36 (Primary) 47N50 (Secondary)
DDC Class
510: Mathematik
530: Physik