On spectral estimates for the Schrödinger operators in global dimension 2
G. RozenblumDepartment of Mathematics, Chalmers University of Technology and The University of Gothenburg S-412 96, Gothenburg, SwedenMichael SolomyakDepartment of Mathematics, Weizmann Institute of Science, Rehovot, Israel
2014en
ABI
Abstract
The problem of finding eigenvalue estimates for the Schrödinger 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 $\mathbb {Z}^2$.
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