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Algebra i Analiz, 2001, Volume 13, Issue 5, Pages 197–240 (Mi aa968)  

This article is cited in 25 scientific papers (total in 25 papers)

Research Papers

Absolute continuity of the spectrum for the Schrödinger operator with potential supported by a periodic system of hypersurfaces

T. A. Suslina, R. G. Shterenberg

St. Petersburg State University, Faculty of Physics

Full text: PDF file (1695 kB)

English version:
St. Petersburg Mathematical Journal, 2002, 13:5, 859–891

Bibliographic databases:
Received: 27.03.2001

Citation: T. A. Suslina, R. G. Shterenberg, “Absolute continuity of the spectrum for the Schrödinger operator with potential supported by a periodic system of hypersurfaces”, Algebra i Analiz, 13:5 (2001), 197–240; St. Petersburg Math. J., 13:5 (2002), 859–891

Citation in format AMSBIB
\Bibitem{SusSht01}
\by T.~A.~Suslina, R.~G.~Shterenberg
\paper Absolute continuity of the spectrum for the Schr\"odinger operator with potential supported by a~periodic system of hypersurfaces
\jour Algebra i Analiz
\yr 2001
\vol 13
\issue 5
\pages 197--240
\mathnet{http://mi.mathnet.ru/aa968}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1882869}
\zmath{https://zbmath.org/?q=an:1068.35122}
\transl
\jour St. Petersburg Math. J.
\yr 2002
\vol 13
\issue 5
\pages 859--891


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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. Suslina T.A., “On the absence of eigenvalues of a periodic matrix Schrödinger operator in a layer”, Russ. J. Math. Phys., 8:4 (2001), 463–486  mathscinet  zmath  isi
    2. Kuchment P., “Graph models for waves in thin structures”, Waves Random Media, 12:4 (2002), R1–R24  crossref  mathscinet  zmath  adsnasa  isi
    3. L. I. Danilov, “O spektre dvumernykh periodicheskikh operatorov Shredingera i Diraka”, Izv. IMI UdGU, 2002, no. 3(26), 3–98  mathnet
    4. 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
    5. J. Math. Sci. (N. Y.), 136:2 (2006), 3826–3831  mathnet  crossref  mathscinet  zmath
    6. M. Tikhomirov, N. Filonov, “Absolute continuity of an even periodic Schrödinger operator with nonsmooth coefficients”, St. Petersburg Math. J., 16:3 (2005), 583–589  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. 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
    9. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    10. 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
    11. Exner P., “Leaky quantum graphs: A review”, Analysis on Graphs and its Applications, Proceedings of Symposia in Pure Mathematics, 77, 2008, 523–564  crossref  mathscinet  zmath  isi
    12. 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
    13. Danilov L.I., “On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator”, J. Phys. A, 42:27 (2009), 275204, 20 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. 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
    15. Danilov L.I., “On absolute continuity of the spectrum of three- and four-dimensional periodic Schrodinger operators”, Journal of Physics A-Mathematical and Theoretical, 43:21 (2010), 215201  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Danilov L.I., “On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator”, Integral Equations Operator Theory, 71:4 (2011), 535–556  crossref  mathscinet  zmath  isi  elib  scopus
    17. Eremin D.A., Popov I.Yu., “Kvantovoe koltso s provodnikom:model dvukhchastichnoi zadachi”, Nanosistemy: fizika, khimiya, matematika, 2:2 (2011), 15–31  zmath  elib
    18. I. Kachkovskiǐ, “Stein–Tomas theorem for a torus and the periodic Schrödinger operator with singular potential”, St. Petersburg Math. J., 24:6 (2013), 939–948  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    19. L. I. Danilov, “O spektre periodicheskogo operatora Shredingera s potentsialom iz prostranstva Morri”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 25–47  mathnet
    20. 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
    21. Behrndt J. Langer M. Lotoreichik V., “Schrodinger Operators with Delta and Delta `-Potentials Supported on Hypersurfaces”, Ann. Henri Poincare, 14:2 (2013), 385–423  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    22. Behrndt J., Grubb G., Langer M., Lotoreichik V., “Spectral Asymptotics For Resolvent Differences of Elliptic Operators With Delta and Delta `-Interactions on Hypersurfaces”, J. Spectr. Theory, 5:4 (2015), 697–729  crossref  mathscinet  zmath  isi  elib  scopus
    23. Exner P. Kovarik H., Quantum Waveguides, Theoretical and Mathematical Physics, Springer-Verlag Berlin, 2015, 1–382  crossref  mathscinet  isi
    24. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    25. V. S. Rabinovich, “Essential Spectrum of Schrödinger Operators with $\delta$-Interactions on Unbounded Hypersurfaces”, Math. Notes, 102:5 (2017), 698–709  mathnet  crossref  crossref  mathscinet  isi  elib
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