Magnetic rings
Abstract
We study functional and spectral properties of perturbations of the magnetic Laplace operator on the circle. 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 the two-dimensional Euclidean space and, on the circle, a sharp interpolation inequality and a sharp Keller-Lieb-Thirring inequality.
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