Norm resolvent convergence to magnetic Schrodinger operators with point interactions

The Schrodinger operator with delta -like magnetic field at the origin in two dimensions is not essentially self-adjoint. It has the deficiency indices (2, 2) and each self-adjoint extension is realized as a differential operator with some boundary conditions at the origin. We here consider Schrodinger operators with magnetic fields of small support and study the norm resolvent convergence to Schrodinger operator with delta -like magnetic field. We are concerned with the boundary conditions realized in the limit when the support shrinks. The results obtained heavily depend on the total flux of magnetic field and on the resonance space at zero energy, and the proof is based on the analysis at low energy for resolvents of Schrodinger operators with magnetic potentials slowly falling off at infinity.