Spectral Approximation of Generalized Schrödinger Operators via Approximation of Subwords

Abstract

AbstractWe prove criteria, purely based on finite subwords of the potential, for spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of generalized Schrödinger operators on the discrete line or half-line. In fact, our results are neither limited to Schrödinger or self-adjoint operators, nor to Hilbert space or 1D: By employing localized lower norms, we strongly generalize known results from the self-adjoint case to much more general and non-normal situations, including various configurations of Hamiltonians and further non-self-adjoint models with aperiodic or pseudoergodic potentials, even models with multiple varying diagonals and entries in a Banach space.