Abstract
Let Γ be a simply connected unbounded C2-hypersurface in ℝn such that Γ divides ℝn into two unbounded domains D±. We consider the essential spectrum of Schrödinger operators on ℝn with surface δΓ-interactions which can be written formally as (Formula presented.), where −Δ is the nonnegative Laplacian in ℝn, W ∈ L∞(ℝn) is a real-valued electric potential, δΓ is the Dirac δ-function with the support on the hypersurface Γ and αΓ ∈ L∞(Γ) is a real-valued coupling coefficient depending of the points of Γ. We realize HΓ as an unbounded operator AΓ in L2(ℝn) generated by the Schrödinger operator (Formula presented.) and Robin-type transmission conditions on the hypersurface Γ. We give a complete description of the essential spectrum of AΓ in terms of the limit operators generated by AΓ and the Robin transmission conditions.
Original language | English |
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Pages (from-to) | 698-709 |
Number of pages | 12 |
Journal | Mathematical Notes |
Volume | 102 |
Issue number | 5-6 |
DOIs | |
State | Published - 1 Nov 2017 |
Keywords
- Robin transmission conditions
- essential spectra
- limit operators
- self-adjoint realization
- surface δ-interaction