Negative eigenvalues of non-local Schr\"{o}dinger operators with sign-changing potentials
Spectral Theory
2023-07-13 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
Simon's results on the negative spectrum of recurrent Schr\"{o}dinger operators () are extended to a wider class of potentials and to non-local operators. An example of potental is constructed for which the essential spectrum of two-dimensional Schr\"{o}dinger operator covers the whole axis. Some counterexamples are provided for transient operators () showing that the assumptions on the potential for the validity of the Cwikel-Lieb-Rozenblum estimate can't be improved significantly.
Keywords
Cite
@article{arxiv.2209.12124,
title = {Negative eigenvalues of non-local Schr\"{o}dinger operators with sign-changing potentials},
author = {S. Molchanov and B. Vainberg},
journal= {arXiv preprint arXiv:2209.12124},
year = {2023}
}