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On spectral estimates for the Schrödinger operators in global dimension 2. (English) Zbl 1304.35454
St. Petersbg. Math. J. 25, No. 3, 495-505 (2014) and Algebra Anal. 25, No. 3, 185-199 (2013).
Summary: 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 \( \mathbb Z^2\).
MSC:
35P15 Estimates of eigenvalues in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35R02 PDEs on graphs and networks (ramified or polygonal spaces)
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