Browsing by Author "Parra, Daniel"

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    Spectral asymptotics at thresholds for a Dirac-type operator on Z2
    (2023) Miranda, Pablo; Parra, Daniel; Raikov, Georgi
    In this article, we provide the spectral analysis of a Dirac-type operator on Z(2) by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We prove that it remains bounded outside a single threshold and obtain its main asymptotic term in the unbounded case. Interestingly, we show that the constant in the main asymptotic term encodes the interaction between a flat band and whole non-constant bands. The strategy used is the reduction of the spectral shift function to the eigenvalue counting function of some compact operator which can be studied as a toroidal pseudo-differential operator. (c) 2022 Elsevier Inc. All rights reserved.