  We consider the Dirichlet Laplacian in the half-plane with constant magnetic
field. Due to the translational invariance this operator admits a fiber
decomposition and a family of dis- persion curves, that are real analytic
functions. Each of them is simple and monotically decreasing from positive
infinity to a finite value, which is the corresponding Landau level. These
finite limits are thresholds in the purely absolutely continuous spectrum of
the magnetic Laplacian. We prove a limiting absorption principle for this
operator both outside and at the thresholds. Finally, we establish analytic and
decay properties for functions lying in the absorption spaces. We point out
that the analysis carried out in this paper is rather general and can be
adapted to a wide class of fibered magnetic Laplacians with thresholds in their
spectrum that are finite limits of their band functions.
