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Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 66–69 | Cite as

Essential Spectrum of Schrödinger Operators on Periodic Graphs

  • V. S. Rabinovich
Brief Communications
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Abstract

We give a description of the essential spectra of unbounded operators ℋ q on L2(Γ) determined by the Schrödinger operators −d2/dx2 + q(x) on the edges of Γ and general vertex conditions. We introduce a set of limit operators of ℋ q such that the essential spectrum of ℋ q is the union of the spectra of limit operators. We apply this result to describe the essential spectra of the operators ℋ q with periodic potentials perturbed by terms slowly oscillating at infinity.

Key words

periodic graph Schrödinger operator on a graph limit operator essential spectrum 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto Politécnico NacionalESIME ZacatencoMexico City, the United Mexican StatesMexico

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