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Algebra i Analiz, 2002, Volume 14, Issue 2, Pages 159–206 (Mi aa845)  

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

Research Papers

Absolute continuity of the spectrum of the magnetic Schrödinger operator with a metric in a two-dimensional periodic waveguide

T. A. Suslina, R. G. Shterenberg

St. Petersburg State University, Faculty of Physics

Full text: PDF file (2119 kB)

English version:
St. Petersburg Mathematical Journal, 2003, 14:2, 305–343

Bibliographic databases:
Received: 05.11.2001

Citation: T. A. Suslina, R. G. Shterenberg, “Absolute continuity of the spectrum of the magnetic Schrödinger operator with a metric in a two-dimensional periodic waveguide”, Algebra i Analiz, 14:2 (2002), 159–206; St. Petersburg Math. J., 14:2 (2003), 305–343

Citation in format AMSBIB
\Bibitem{SusSht02}
\by T.~A.~Suslina, R.~G.~Shterenberg
\paper Absolute continuity of the spectrum of the magnetic Schr\"odinger operator with a~metric in a~two-dimensional periodic waveguide
\jour Algebra i Analiz
\yr 2002
\vol 14
\issue 2
\pages 159--206
\mathnet{http://mi.mathnet.ru/aa845}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1925885}
\zmath{https://zbmath.org/?q=an:1057.35024}
\transl
\jour St. Petersburg Math. J.
\yr 2003
\vol 14
\issue 2
\pages 305--343


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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. L. I. Danilov, “The Spectrum of the Two-Dimensional Periodic Schrödinger Operator”, Theoret. and Math. Phys., 134:3 (2003), 392–403  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. R. G. Shterenberg, “Absolute continuity of the spectrum of two-dimensional periodic Schrödinger operators with strongly subordinate magnetic potential”, J. Math. Sci. (N. Y.), 129:4 (2005), 4087–4109  mathnet  crossref  mathscinet  zmath
    3. R. G. Shterenberg, “Schrödinger operator in a periodic waveguide on the plane and quasi-conformal mappings”, J. Math. Sci. (N. Y.), 127:2 (2005), 1936–1956  mathnet  crossref  mathscinet  zmath
    4. Shargorodsky E., Sobolev A. V., “Quasiconformal mappings and periodic spectral problems in dimension two”, J. Anal. Math., 91 (2003), 67–103  crossref  mathscinet  zmath  isi  scopus
    5. L. I. Danilov, “Ob otsutstvii sobstvennykh znachenii v spektre dvumernykh periodicheskikh operatorov Diraka i Shredingera”, Izv. IMI UdGU, 2004, no. 1(29), 49–84  mathnet
    6. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, St. Petersburg Math. J., 17:3 (2006), 409–433  mathnet  crossref  mathscinet  zmath
    7. Friedlander L., Solomyak M., “On the spectrum of narrow periodic waveguides”, Russ. J. Math. Phys., 15:2 (2008), 238  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Shen Zhongwei, Zhao Peihao, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Trans. Amer. Math. Soc., 360:4 (2008), 1741–1758  crossref  mathscinet  zmath  isi  elib  scopus
    9. I. Kachkovskii, N. Filonov, “Absolute continuity of the spectrum of a periodic Schrödinger operator in a multidimensional cylinder”, St. Petersburg Math. J., 21:1 (2010), 95–109  mathnet  crossref  mathscinet  zmath  isi
    10. I. Kachkovskii, N. Filonov, “Absolute continuity of the spectrum of the periodic Scrödinger operator in a layer and in a smooth cylinder”, J. Math. Sci. (N. Y.), 178:3 (2011), 274–281  mathnet  crossref
    11. Bunoiu R., Cardone G., Suslina T., “Spectral approach to homogenization of an elliptic operator periodic in some directions”, Math Methods Appl Sci, 34:9 (2011), 1075–1096  crossref  mathscinet  zmath  isi  elib  scopus
    12. I. Kachkovskii, “Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder”, Funct. Anal. Appl., 47:2 (2013), 104–112  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Vu Hoang Radosz M., “Absence of Bound States For Waveguides in Two-Dimensional Periodic Structures”, J. Math. Phys., 55:3 (2014), 033506  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Fliss S. Joly P., “Solutions of the Time-Harmonic Wave Equation in Periodic Waveguides: Asymptotic Behaviour and Radiation Condition”, Arch. Ration. Mech. Anal., 219:1 (2016), 349–386  crossref  mathscinet  zmath  isi  elib  scopus
    15. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    16. S. A. Nazarov, “The asymptotic behaviour of the scattering matrix in a neighbourhood of the endpoints of a spectral gap”, Sb. Math., 208:1 (2017), 103–156  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    17. Delourme B. Fliss S. Joly P. Vasilevskaya E., “Trapped Modes in Thin and Infinite Ladder Like Domains. Part 1: Existence Results”, Asymptotic Anal., 103:3 (2017), 103–134  crossref  mathscinet  zmath  isi  scopus
    18. S. A. Nazarov, “Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations”, J. Math. Sci. (N. Y.), 243:5 (2019), 746–773  mathnet  crossref
    19. S. A. Nazarov, “Konechnomernye versii operatora Steklova–Puankare dlya obschikh ellipticheskikh kraevykh zadach v oblastyakh s tsilindricheskimi i periodicheskimi vykhodami na beskonechnost”, Tr. MMO, 80, no. 1, MTsNMO, M., 2019, 1–62  mathnet
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