Some remarks on strong unique continuation for the laplace operator and its powers

ABSTRACT

Some spectral properties of magnetic Schrödinger and Dirac operators perturbed by long range magnetic fields are investigated. If the intensity of the field is small enough, a better location of the perturbed spectrum is given. In particular, if the unperturbed spectrum is discrete, we show that the perturbed eigenvalues are given in terms of an absolutely convergent series with respect to a magnetic parameter, from which the usual asymptotic expansion can be derived.