Spectral stability for compact perturbations of Toeplitz matrices

2014/04/03 by Astaburuaga, M. A., Bourget, O., Cortés, V. H. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1404.1035

Abstract

Let f be a regular real-valued non-constant symbol defined on the one dimensional torus \mathbb T. Denote respectively by κ and T, its set of critical points and the associated Toeplitz matrix on l²(\mathbb N). If V is a suitable compact perturbation, we prove that the operator T+V has no singular continuous spectrum and only finite point spectrum away from the set of thresholds f(κ). We also obtain some propagation estimates and apply these results to concrete examples.

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• On the spectral properties of long-range perturbations of a class of block finite difference operators

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