Symmetry Results in Two-Dimensional Inequalities for Aharonov–Bohm Magnetic Fields

We study functional and spectral properties of perturbations of a magnetic second order differential operator on a circle. This operator appears when considering the restriction to the unit circle of a two dimensional Schrödinger operator with the Bohm-Aharonov vector potential. We prove some Hardy’s and sharp Keller-Lieb-Thirring inequalities.