Approximation of magnetic Schrödinger operators with $\delta$-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 $(i\mathrm{\nabla }+A{)}^2+Q+\alpha {\delta }_{\mathrm{\Sigma }}$ by Schrödinger operators with regular potentials in the norm resolvent sense. This is done for $\mathrm{\Sigma }$ 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, $\mathrm{\Sigma }$ can be a graph in ${\mathbb{R}}^2$ or the boundary of a piecewise $C^2$-domain. Moreover, spectral implications of the mentioned convergence result are discussed.