Spectral stability of Schroedinger operators with subordinated complex potentials
Spectral Theory
2018-11-26 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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.
Cite
@article{arxiv.1506.01617,
title = {Spectral stability of Schroedinger operators with subordinated complex potentials},
author = {Luca Fanelli and David Krejcirik and Luis Vega},
journal= {arXiv preprint arXiv:1506.01617},
year = {2018}
}
Comments
18 pages; version accepted for publication in J. Spectr. Theory; statement and proof of Theorem 3 corrected