On spectral estimates for the Schrödinger operators in global dimension 2

Rozenblum, G.; Solomyak, M.

doi:10.1090/S1061-0022-2014-01301-5

On spectral estimates for the Schrödinger operators in global dimension 2
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by G. Rozenblum and M. Solomyak

St. Petersburg Math. J. 25 (2014), 495-505

DOI: https://doi.org/10.1090/S1061-0022-2014-01301-5

Published electronically: May 16, 2014

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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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