Magnetic rings

We study functional and spectral properties of perturbations of the operator −(∂s +ia)2 in L2(S1). This operator appears when considering the restriction to the unit circle of a two dimensional Schr ̈odinger operator with the Bohm-Aharonov vector potential. We prove a Hardy-type inequality on R2 and, on S1, a sharp interpolation inequality and a sharp Keller-Lieb-Thirring inequality.