Spectral approximation of generalized Schr\"odinger operators via approximation of subwords

TL;DR

This paper develops criteria based on finite subwords of potentials to approximate spectra and pseudospectra of generalized Schr"odinger operators, applicable beyond traditional settings like self-adjoint or 1D cases.

Contribution

It introduces novel criteria for spectral and pseudospectral approximation using finite subwords, extending applicability to non-self-adjoint and higher-dimensional operators.

Findings

Spectral inclusion criteria based on finite subwords

Hausdorff approximation of spectra and pseudospectra

Applicability beyond Schr"odinger and self-adjoint operators

Abstract

We demonstrate criteria, purely based on finite subwords of the potential, to guarantee spectral inclusion as well as Hausdorff approximation of pseudospectra or even spectra of generalized Schr\"odinger operators on the discrete line or half-line. In fact, our results are neither limited to Schr\"odinger or self-adjoint operators, nor to Hilbert space or 1D.