Magnetic Schrödinger operators with delta-type potentials

We consider the magnetic anisotropic Schrödinger operator on (Formula presented.) 1 (Formula presented.) where (Formula presented.) is the vector potential of the magnetic field and W(x) is the scalar potential of the electric field. We assume that a_j and ϱ_ij are real-valued functions belonging to the space (Formula presented.) of bounded with first derivatives on (Formula presented.) functions, whereas (Formula presented.) is a complex-valued electric potential. Let Σ be a C²-hypersurface in (Formula presented.) dividing (Formula presented.) on two open domains Ω_± with common boundary Σ. We assume that Σ is a closed C²-hypersurface or unbounded hypersurface of bounded geometry. We consider the magnetic Schrödinger operator (Formula presented.) with singular potentials W_s with supports on Σ. We associate with (Formula presented.) an unbounded operator (Formula presented.) in (Formula presented.) generated by H_{ϱ,a, W} with domain in H²(Ω₊) ⊕ H²(Ω₋) consisting of functions satisfying interaction conditions on Σ. We study the self-adjointness of the operator (Formula presented.) and its Fredholm properties. Moreover, we consider the spectral problem 2 (Formula presented.) and reduce this problem to a spectral problem for some boundary pseudodifferential operators on Σ. We describe the domains in (Formula presented.) where problem (2) has the discrete spectrum.