Stable approximation and spectral theory
Citation Link: https://doi.org/10.15480/882.13177
Publikationstyp
Doctoral Thesis
Date Issued
2024
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2024-07-03
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2024)
This work presents methods for the approximation of solutions of linear systems involving band-dominated operators on l^p spaces.
In particular, conditions for the applicability of the periodic finite section method are found and
a method for the approximation of pseudospectra of band operators is derived.
Additionally, Dirichlet eigenvalues of 1D discrete Schrödinger operators are studied.
For integer-valued potential and a subclass of periodic potentials the absence of Dirichlet eigenvalues at energy 0 is proven.
For Sturmian potentials, the spectral convergence for the periodic approximation and a method for a precise localization of Dirichlet eigenvalues are derived.
In particular, conditions for the applicability of the periodic finite section method are found and
a method for the approximation of pseudospectra of band operators is derived.
Additionally, Dirichlet eigenvalues of 1D discrete Schrödinger operators are studied.
For integer-valued potential and a subclass of periodic potentials the absence of Dirichlet eigenvalues at energy 0 is proven.
For Sturmian potentials, the spectral convergence for the periodic approximation and a method for a precise localization of Dirichlet eigenvalues are derived.
Subjects
Spectral Theory
Approximation Methods
Finite Section Method
Discrete Schrödinger Operators
Fibonacci Hamiltonian
DDC Class
510: Mathematics
Loading...
Name
Riko_Ukena-Stable-Approximation-and-Spectral-Theory.pdf
Size
2.55 MB
Format
Adobe PDF