English

On spectral estimates for the Schr\"odinger operators in global dimension 2

Spectral Theory 2012-09-03 v1

Abstract

The problem of finding eigenvalue estimates for the Schr\"odinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently. We discuss these results and establish their counterparts for the operators on the combinatorial and metric graphs corresponding to the lattice Z^2.

Keywords

Cite

@article{arxiv.1208.6372,
  title  = {On spectral estimates for the Schr\"odinger operators in global dimension 2},
  author = {Grigori Rozenblum and Michael Solomyak},
  journal= {arXiv preprint arXiv:1208.6372},
  year   = {2012}
}