We prove that the spectrum of Schr\"odinger 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 Schr\"odinger operators in all dimensions under various alternative hypotheses, still allowing complex-valued potentials with critical singularities.

Spectral stability of Schrödinger operators with subordinated complex potentials / Fanelli, L.; Krejcirik, D.; Vega, L.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - STAMPA. - 8:2(2018), pp. 575-604. [10.4171/JST/208]

Spectral stability of Schrödinger operators with subordinated complex potentials

Fanelli L.;Krejcirik D.
;
Vega L.
2018

Abstract

We prove that the spectrum of Schr\"odinger 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 Schr\"odinger operators in all dimensions under various alternative hypotheses, still allowing complex-valued potentials with critical singularities.
2018
non self-adjoint schrodinger operator, subordinated complex potentials
01 Pubblicazione su rivista::01a Articolo in rivista
Spectral stability of Schrödinger operators with subordinated complex potentials / Fanelli, L.; Krejcirik, D.; Vega, L.. - In: JOURNAL OF SPECTRAL THEORY. - ISSN 1664-039X. - STAMPA. - 8:2(2018), pp. 575-604. [10.4171/JST/208]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1126121
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