We prove that the spectrum of Schrödinger 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 Schrödinger operators in all dimensions under various alternative hypotheses, still allowing complex-valued potentials with critical singularities.
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Luca Fanelli, David Krejčiřík, Luis Vega, Spectral stability of Schrödinger operators with subordinated complex potentials. J. Spectr. Theory 8 (2018), no. 2, pp. 575–604DOI 10.4171/JST/208