Scattering for the fractional magnetic Schrödinger operators

In this paper, we prove the existence of the scattering operator for the fractional magnetic Schrödinger operators. In order to do this, we construct the fractional distorted Fourier transforms with magnetic potentials. Applying the properties of the distorted Fourier transforms, the existence and the asymptotic completeness of the wave operators are obtained. Furthermore, we prove the absence of positive eigenvalues for fractional magnetic Schrödinger operators.