On Spectral Estimates for the Schrodinger Operators in Global Dimension 2

Journal article, 2014

The problem of finding eigenvalue estimates for the Schrodinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently. In the paper, these results are discussed, and their counterparts are established for the operator on the combinatorial and metric graphs corresponding to the lattice Z(2).