Essential Spectrum of Schrödinger Operators on Periodic Graphs

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Abstract

We give a description of the essential spectra of unbounded operators ℋq 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 ℋq such that the essential spectrum of ℋq is the union of the spectra of limit operators. We apply this result to describe the essential spectra of the operators ℋq with periodic potentials perturbed by terms slowly oscillating at infinity.

Original languageEnglish
Pages (from-to)66-69
Number of pages4
JournalFunctional Analysis and its Applications
Volume52
Issue number1
DOIs
StatePublished - 1 Jan 2018

Keywords

  • Schrödinger operator on a graph
  • essential spectrum
  • limit operator
  • periodic graph

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