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Item type:Publication, Access status: with files , Stable approximation and spectral theory(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.Publicationtype: Doctoral Thesis41 162