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On spectral estimates for the Schrödinger operators in global dimension 2

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. We discuss these results and establish their counterparts for the operators on the combinatorial and metric graphs corresponding to the lattice Z^2.

preprint2012arXivOpen access
Grigori RozenblumMichael Solomyak
math.SP
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Grigori RozenblumMichael Solomyak

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