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

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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. Birman^a, A. Laptev^b, T. A. Suslina^a

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

Full-text PDF (1749 kB) Citations (12)

Received: 10.03.2000

Bibliographic databases:

Document Type: Article

Language: Russian

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://mathscinet.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

Linking options:

https://www.mathnet.ru/eng/aa1115

https://www.mathnet.ru/eng/aa/v12/i4/p36

This publication is cited in the following 12 articles:

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
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
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.
Miao Dong, “The discrete spectrum of the periodic Maxwell operator perturbed by a decreasing potential”, J. Math. Phys., 49:6 (2008), 063511, 24 pp.
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
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
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
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
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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