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Algebra i Analiz, 2013, Volume 25, Issue 3, Pages 185–199 (Mi aa1338)  

This article is cited in 4 scientific papers (total in 4 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

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.

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English version:
St. Petersburg Mathematical Journal, 2014, 25:3, 495–505

Bibliographic databases:

Received: 02.09.2012
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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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\paper On spectral estimates for the Schr\"odinger operators in global dimension~2
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\vol 25
\issue 3
\pages 185--199
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J. P. Chen, S. Molchanov, A. Teplyaev, “Spectral dimension and Bohr's formula for Schrtsdinger operators on unbounded fractal spaces”, J. Phys. A, 48:39 (2015), 395203, 27 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    2. Kapitanski L., Laptev A., “On continuous and discrete Hardy inequalities”, J. Spectr. Theory, 6:4 (2016), 837–858  crossref  mathscinet  zmath  isi  scopus
    3. V. Bach, W. de Siqueira Pedra, S. N. Lakaev, “Bounds on the discrete spectrum of lattice Schrödinger operators”, J. Math. Phys., 59:2 (2018), 022109  crossref  mathscinet  zmath  isi  scopus
    4. G. V. Rozenblyum, “O matematicheskikh rabotakh Mikhaila Zakharovicha Solomyaka”, Algebra i analiz, 30:3 (2018), 3–29  mathnet  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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