Half-line compressions and finite sections of discrete Schrödinger operators with integer-valued potentials

Publikationstyp
Journal Article
Date Issued
2023-06-15
Sprache
English
Author(s)
Lindner, Marko  orcid-logo
Ukena, Riko  orcid-logo
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/13692
Journal
Journal of mathematical analysis and applications  
Volume
522
Issue
2
Article Number
126984
Citation
Journal of Mathematical Analysis and Applications 522 (2): 126984 (2023-06-15)
Publisher DOI
10.1016/j.jmaa.2022.126984
Scopus ID
2-s2.0-85146080313
ArXiv ID
2208.04015v3
Publisher
Elsevier
We study 1D discrete Schrödinger operators H with integer-valued potential and show that, (i), invertibility (in fact, even just Fredholmness) of H always implies invertibility of its half-line compression H₊ (zero Dirichlet boundary condition, i.e. matrix truncation). In particular, the Dirichlet eigenvalues avoid zero -- and all other integers. We use this result to conclude that, (ii), the finite section method (approximate inversion via finite and growing matrix truncations) is applicable to H as soon as H is invertible. The same holds for H₊.
Subjects
Mathematics - Functional Analysis
Mathematics - Functional Analysis
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Spectral Theory
47N40
47B36
47B93
65J10
DDC Class
510: Mathematik