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 $\delta$ -potential that is formally given by ${(i\nabla +A)}^2+Q+\alpha {\delta }_{\Sigma }$ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for $\Sigma$ being the finite union of $C^2$ -hypersurfaces, for coefficients A, Q, and $\alpha$ under almost minimal assumptions such that the associated quadratic forms are closed and sectorial, and Q and $\alpha$ are allowed to be complex-valued functions. In particular, $\Sigma$ can be a graph in $R^2$ or the boundary of a piecewise $C^2$ -domain. Moreover, spectral implications of the mentioned convergence result are discussed.