Spectral stability of Schrödinger operators with subordinated complex potentials

  • Luca Fanelli

    Università di Roma La Sapienza, Italy
  • David Krejčiřík

    Nuclear Physics Institute, Rez, and Czech Technical University, Prague, Czechia
  • Luis Vega

    Universidad del Pais Vasco, Bilbao, Spain and Basque Center for Applied Mathematics, Bilbao, Spain
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Abstract

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.

Cite this article

Luca Fanelli, David Krejčiřík, Luis Vega, Spectral stability of Schrödinger operators with subordinated complex potentials. J. Spectr. Theory 8 (2018), no. 2, pp. 575–604

DOI 10.4171/JST/208