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Algebra i Analiz, 2013, Volume 25, Issue 3, Pages 185–199 (Mi aa1338)  
This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

On spectral estimates for the Schrödinger operators in global dimension 2

G. Rozenbluma, M. Solomyakb

a Department of Mathematics, Chalmers University of Technology and The University of Gothenburg, S-412, 96, Gothenburg, Sweden
b Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Full-text PDF (305 kB) Citations (9)
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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 $\mathbb Z^2$.
Keywords: eigenvalue estimates, Schrödinger operator, metric graphs, local dimension.
Received: 02.09.2012
English version:
St. Petersburg Mathematical Journal, 2014, Volume 25, Issue 3, Pages 495–505
DOI: https://doi.org/10.1090/S1061-0022-2014-01301-5
Bibliographic databases:
Document Type: Article
Language: English
Citation: G. Rozenblum, M. Solomyak, “On spectral estimates for the Schrödinger operators in global dimension 2”, Algebra i Analiz, 25:3 (2013), 185–199; St. Petersburg Math. J., 25:3 (2014), 495–505
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    References:49
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