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Essential Spectrum of Schrödinger Operators on Periodic Graphs

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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.

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Authors and Affiliations

  1. Instituto Politécnico Nacional, ESIME Zacatenco, Mexico City, the United Mexican States, Mexico

    V. S. Rabinovich

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  1. V. S. Rabinovich
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Correspondence to V. S. Rabinovich.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 1, pp. 80–84, 2018

Original Russian Text Copyright © by V. S. Rabinovich

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Rabinovich, V.S. Essential Spectrum of Schrödinger Operators on Periodic Graphs. Funct Anal Its Appl 52, 66–69 (2018). https://doi.org/10.1007/s10688-018-0210-y

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  • DOI: https://doi.org/10.1007/s10688-018-0210-y

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