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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 6(318), Pages 177–178 (Mi umn910)  

This article is cited in 18 scientific papers (total in 19 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

The Schrödinger operator on graphs and topology

S. P. Novikov

University of Maryland

DOI: https://doi.org/10.4213/rm910

Full text: PDF file (231 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:6, 1320–1321

Bibliographic databases:

Document Type: Article
MSC: 34L40, 34L15, 47A10
Accepted: 25.11.1997

Citation: S. P. Novikov, “The Schrödinger operator on graphs and topology”, Uspekhi Mat. Nauk, 52:6(318) (1997), 177–178; Russian Math. Surveys, 52:6 (1997), 1320–1321

Citation in format AMSBIB
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\by S.~P.~Novikov
\paper The Schr\"odinger operator on graphs and topology
\jour Uspekhi Mat. Nauk
\yr 1997
\vol 52
\issue 6(318)
\pages 177--178
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\crossref{https://doi.org/10.4213/rm910}
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\zmath{https://zbmath.org/?q=an:0925.34114}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1997RuMaS..52.1320N}
\transl
\jour Russian Math. Surveys
\yr 1997
\vol 52
\issue 6
\pages 1320--1321
\crossref{https://doi.org/10.1070/RM1997v052n06ABEH002181}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. “Sergei Petrovich Novikov (on his 60th birthday)”, Russian Math. Surveys, 54:1 (1999), 1–7  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. S. P. Novikov, A. S. Schwarz, “Discrete Lagrangian systems on graphs. Symplectic-topological properties”, Russian Math. Surveys, 54:1 (1999), 258–259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. L. O. Chekhov, “A spectral problem on graphs and $L$-functions”, Russian Math. Surveys, 54:6 (1999), 1197–1232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. S. P. Novikov, “Difference Schrödinger Operators”, Proc. Steklov Inst. Math., 224 (1999), 250–265  mathnet  mathscinet  zmath
    5. Kostrykin, V, “Kirchhoff's rule for quantum wires”, Journal of Physics A-Mathematical and General, 32:4 (1999), 595  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. L. O. Chekhov, N. V. Puzyrnikova, “Integrable systems on graphs”, Russian Math. Surveys, 55:5 (2000), 992–994  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. Proc. Steklov Inst. Math., 231 (2000), 1–41  mathnet  mathscinet  zmath
    8. Kuchment, P, “Convergence of spectra of mesoscopic systems collapsing onto a graph”, Journal of Mathematical Analysis and Applications, 258:2 (2001), 671  crossref  mathscinet  zmath  isi  scopus
    9. Hurt, NE, “The prime geodesic theorem and quantum mechanics on finite volume graphs: A review”, Reviews in Mathematical Physics, 13:12 (2001), 1459  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. L. O. Chekhov, “Integrable deformations of systems on graphs with loops”, Russian Math. Surveys, 57:3 (2002), 587–588  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Kuchment, P, “Graph models for waves in thin structures”, Waves in Random Media, 12:4 (2002), R1  crossref  mathscinet  zmath  adsnasa  isi
    12. Kuchment, P, “Differential operators on graphs and photonic crystals”, Advances in Computational Mathematics, 16:2–3 (2002), 263  crossref  mathscinet  zmath  isi  elib  scopus
    13. Blumel, R, “Explicitly solvable cases of one-dimensional quantum chaos”, Physical Review Letters, 88:4 (2002), 044101  crossref  adsnasa  isi  scopus
    14. Dabaghian, Y, “Explicit analytical solution for scaling quantum graphs”, Physical Review E, 68:5 (2003), 055201  crossref  mathscinet  adsnasa  isi  scopus
    15. Adler, VE, “Cauchy problem for integrable discrete equations on quad-graphs”, Acta Applicandae Mathematicae, 84:2 (2004), 237  crossref  mathscinet  zmath  isi  elib
    16. Kuchment, P, “Quantum graphs: I. Some basic structures”, Waves in Random Media, 14:1 (2004), S107  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Kuchment, P, “Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs”, Journal of Physics A-Mathematical and General, 38:22 (2005), 4887  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. Kuchment P., “Quantum graphs: an introduction and a brief survey”, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, 77, 2008, 291–312  crossref  mathscinet  zmath  isi
    19. P. G. Grinevich, S. P. Novikov, “Discrete $SL_n$-connections and self-adjoint difference operators on two-dimensional manifolds”, Russian Math. Surveys, 68:5 (2013), 861–887  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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