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 language | English |
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Pages (from-to) | 66-69 |
Number of pages | 4 |
Journal | Functional Analysis and its Applications |
Volume | 52 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2018 |
Keywords
- Schrödinger operator on a graph
- essential spectrum
- limit operator
- periodic graph