Approximation of magnetic Schrödinger operators with δ-interactions supported on networks

This paper deals with the approximation of a magnetic Schrödinger operator with a singular δ-potential that is formally given by (i∇+A)2+Q+αδΣ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for Σ being the finite union of C2-hypersurfaces, for coefficients A, Q, and α under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and Q and α are allowed to be complex-valued functions. In particular, Σ can be a graph in R2 or the boundary of a piecewise C2-domain. Moreover, spectral implications of the mentioned convergence result are discussed.