Spectral bounds for non-smooth perturbations of the Landau Hamiltonian (Q6144556)

The Landeau Hamiltonian (LH) is a self-adjoint realization (in the set of square integrable functions on the Euclidean plan) of an explicit second order partial differential operator. The purpose of the author is to provide some spectral properties of the LH perturbed by a pseudo-differential operator with non-smooth Weyl symbol in a subset of tempered distributions. Essentially, he provides an upper bound of the number of bound states in a gap of the essential spectrum.