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

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