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Algebra i Analiz, 2000, Volume 12, Issue 4, Pages 36–78 (Mi aa1115)  

This article is cited in 12 scientific papers (total in 12 papers)

Research Papers

The discrete spectrum of a two-dimensional second-order periodic elliptic operator perturbed by a decreasing potential. I. A semi-infinite gap

M. Sh. Birmana, A. Laptevb, T. A. Suslinaa

a St. Petersburg State University, Faculty of Physics
b Royal Institute of Technology, Stockholm, Sweden

Full text: PDF file (1749 kB)

English version:
St. Petersburg Mathematical Journal, 2001, 12:4, 535–567

Bibliographic databases:

Received: 10.03.2000

Citation: M. Sh. Birman, A. Laptev, T. A. Suslina, “The discrete spectrum of a two-dimensional second-order periodic elliptic operator perturbed by a decreasing potential. I. A semi-infinite gap”, Algebra i Analiz, 12:4 (2000), 36–78; St. Petersburg Math. J., 12:4 (2001), 535–567

Citation in format AMSBIB
\Bibitem{BirLapSus00}
\by M.~Sh.~Birman, A.~Laptev, T.~A.~Suslina
\paper The discrete spectrum of a~two-dimensional second-order periodic elliptic operator perturbed by a~decreasing potential.~I. A~semi-infinite gap
\jour Algebra i Analiz
\yr 2000
\vol 12
\issue 4
\pages 36--78
\mathnet{http://mi.mathnet.ru/aa1115}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1793617}
\zmath{https://zbmath.org/?q=an:1070.47041}
\transl
\jour St. Petersburg Math. J.
\yr 2001
\vol 12
\issue 4
\pages 535--567


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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. Birman M.S., Solomyak M., “On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential”, J. Anal. Math., 83 (2001), 337–391  crossref  mathscinet  zmath  isi  scopus
    2. Birman M., Suslina T., “Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics”, Systems, Approximation, Singular Integral Operators, and Related Topics, Operator Theory : Advances and Applications, 129, 2001, 71–107  crossref  mathscinet  zmath  adsnasa  isi
    3. T. A. Suslina, “Descrete spectrum of the two-dimensional periodic second order elliptic operator perturbed by a decaying potential. II. Internal gaps”, St. Petersburg Math. J., 15:2 (2004), 249–287  mathnet  crossref  mathscinet  zmath
    4. M. Sh. Birman, T. A. Suslina, “Periodic differential operators of second order. Threshold properties and averagings”, St. Petersburg Math. J., 15:5 (2004), 639–714  mathnet  crossref  mathscinet  zmath
    5. Bentosela F., Duclos P., Exner P., “Absolute continuity in periodic thin tubes and strongly coupled leaky wires”, Lett. Math. Phys., 65:1 (2003), 75–82  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. V. S. Buslaev, M. Z. Solomyak, D. R. Yafaev, “Mikhail Shlemovich Birman (on the Occasion of his 75th Birthday)”, St. Petersburg Math. J., 16:1 (2005), 1–8  mathnet  crossref  mathscinet  zmath
    7. Exner P., Kondej S., “Strong-coupling asymptotic expansion for Schrödinger operators with a singular interaction supported by a curve in $\mathbb R^3$”, Rev. Math. Phys., 16:5 (2004), 559–582  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Miao Dong, “Eigenvalue branches of the perturbed Maxwell operator $M+\lambda D$ in a gap of $\sigma(M)$”, J. Math. Phys., 49:11 (2008), 113508, 33 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Miao Dong, “The discrete spectrum of the periodic Maxwell operator perturbed by a decreasing potential”, J. Math. Phys., 49:6 (2008), 063511, 24 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Frank R.L., Simon B., Weidl T., “Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states”, Comm. Math. Phys., 282:1 (2008), 199–208  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38  mathnet  crossref  mathscinet  zmath  isi  elib
    12. Frank R.L., Simon B., “Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices”, Duke Math J, 157:3 (2011), 461–493  crossref  mathscinet  zmath  isi  scopus
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