• Corpus ID: 233004459

Finite section method for aperiodic Schrödinger operators

@article{Gabel2021FiniteSM,
title={Finite section method for aperiodic Schr{\"o}dinger operators},
author={Fabian Gabel and Dennis Gallaun and Julian Grossmann and Riko Ukena},
journal={ArXiv},
year={2021},
volume={abs/2104.00711}
}
We consider discrete Schrödinger operators with aperiodic potentials given by a Sturmian word, which is a natural generalisation of the FibonacciHamiltonian. 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. By using periodic approximations, we find a necessary and sufficient condition for…
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