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On spectral estimates for the Schrödinger operators in global dimension 2


Authors: G. Rozenblum and M. Solomyak
Original publication: Algebra i Analiz, tom 25 (2013), nomer 3.
Journal: St. Petersburg Math. J. 25 (2014), 495-505
MSC (2010): Primary 35P15
DOI: https://doi.org/10.1090/S1061-0022-2014-01301-5
Published electronically: May 16, 2014
MathSciNet review: 3184603
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

G. Rozenblum
Affiliation: Department of Mathematics, Chalmers University of Technology and The University of Gothenburg S-412 96, Gothenburg, Sweden
Email: grigori@chalmers.se

M. Solomyak
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Email: michail.solomyak@weizmann.ac.il

DOI: https://doi.org/10.1090/S1061-0022-2014-01301-5
Keywords: Eigenvalue estimates, Schr\"odinger operator, metric graphs, local dimension
Received by editor(s): September 2, 2012
Published electronically: May 16, 2014
Dedicated: To Boris Mikhaĭlovich Makarov, on the occasion of his 80th birthday
Article copyright: © Copyright 2014 American Mathematical Society

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