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Zap. Nauchn. Sem. POMI, 2003, Volume 303, Pages 279–320 (Mi znsl912)  

This article is cited in 14 scientific papers (total in 14 papers)

Absolute continuity of the spectrum of two-dimensional periodic Schrödinger operators with strongly subordinate magnetic potential

R. G. Shterenberg

Saint-Petersburg State University

Abstract: A two-dimensional periodic magnetic Schrödinger operator with variable metric is considered. It is shown that under the condition of strong subordination of the magnetic potential the spectrum of the operator is absolutely continuous. A similar result concerning the Schrödinger operator in a simply connected periodic waveguide is also formulated.

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English version:
Journal of Mathematical Sciences (New York), 2005, 129:4, 4087–4109

Bibliographic databases:

UDC: 517.948
Received: 10.07.2003

Citation: R. G. Shterenberg, “Absolute continuity of the spectrum of two-dimensional periodic Schrödinger operators with strongly subordinate magnetic potential”, Investigations on linear operators and function theory. Part 31, Zap. Nauchn. Sem. POMI, 303, POMI, St. Petersburg, 2003, 279–320; J. Math. Sci. (N. Y.), 129:4 (2005), 4087–4109

Citation in format AMSBIB
\Bibitem{Sht03}
\by R.~G.~Shterenberg
\paper Absolute continuity of the spectrum of two-dimensional periodic Schr\"odinger operators with strongly subordinate magnetic potential
\inbook Investigations on linear operators and function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 303
\pages 279--320
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl912}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2037543}
\zmath{https://zbmath.org/?q=an:1148.35338}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 129
\issue 4
\pages 4087--4109
\crossref{https://doi.org/10.1007/s10958-005-0344-3}


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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, “Ob otsutstvii sobstvennykh znachenii v spektre dvumernykh periodicheskikh operatorov Diraka i Shredingera”, Izv. IMI UdGU, 2004, no. 1(29), 49–84  mathnet
    2. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    3. Friedlander L., Solomyak M., “On the spectrum of narrow periodic waveguides”, Russian Journal of Mathematical Physics, 15:2 (2008), 238–242  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Shen Zh., Zhao P., “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Trans Amer Math Soc, 360:4 (2008), 1741–1758  crossref  mathscinet  zmath  isi  elib  scopus
    5. Danilov L.I., “On absolute continuity of the spectrum of a periodic magnetic Schrodinger operator”, Journal of Physics A-Mathematical and Theoretical, 42:27 (2009), 275204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. 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
    7. 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
    8. 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
    9. 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
    10. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera”, Izv. IMI UdGU, 2013, no. 1(41), 78–95  mathnet
    11. 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
    12. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera. II”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 3–28  mathnet
    13. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41  mathnet  crossref  elib
    14. Filonov N., Kachkovskiy I., “On the Structure of Band Edges of 2-Dimensional Periodic Elliptic Operators”, Acta Math., 221:1 (2018), 59–80  crossref  mathscinet  zmath  isi  scopus
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