Spectral stability of Schroedinger operators with subordinated complex potentials

We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing the method of multipliers, we also establish the absence of point spectrum for Schroedinger operators in all dimensions under various alternative hypotheses, still allowing complex-valued potentials with critical singularities.