Essential Spectrum of Schrödinger Operators on Periodic Graphs

Resumo

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.