Schrödinger operators with interactions on unbounded hypersurfaces

We consider Schrödinger operators H = −Δ + W + W_s on (Formula presented.) with regular potentials (Formula presented.) and singular potentials (Formula presented.) with supports on unbounded enough smooth hypersurfaces Γ. In particular, we consider singular potentials that are linear combinations of δ−functions on Γ and its normal derivatives. We consider extensions of H as symmetric operators in (Formula presented.) with domain (Formula presented.) to self-adjoint operators (Formula presented.) in (Formula presented.). These extensions are realized as operators of transmission problems for −Δ + W in the space (Formula presented.) with some transmission conditions on Γ. Applying this approach, we obtain an effective description of essential spectra of the described Schrödinger operators.