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Algebra i Analiz, 1998, Volume 10, Issue 4, Pages 1–36 (Mi aa1018)  

This article is cited in 34 scientific papers (total in 34 papers)

Research Papers

Absolute continuity of a two-dimensional periodic magnetic Hamiltonian with discontinuous vector potential

M. Sh. Birman, T. A. Suslina

St. Petersburg State University, Faculty of Physics

Full text: PDF file (1123 kB)

English version:
St. Petersburg Mathematical Journal, 1999, 10:4, 579–601

Bibliographic databases:

Received: 26.01.1998

Citation: M. Sh. Birman, T. A. Suslina, “Absolute continuity of a two-dimensional periodic magnetic Hamiltonian with discontinuous vector potential”, Algebra i Analiz, 10:4 (1998), 1–36; St. Petersburg Math. J., 10:4 (1999), 579–601

Citation in format AMSBIB
\Bibitem{BirSus98}
\by M.~Sh.~Birman, T.~A.~Suslina
\paper Absolute continuity of a two-dimensional periodic magnetic Hamiltonian with discontinuous vector potential
\jour Algebra i Analiz
\yr 1998
\vol 10
\issue 4
\pages 1--36
\mathnet{http://mi.mathnet.ru/aa1018}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1654063}
\zmath{https://zbmath.org/?q=an:0922.35101}
\transl
\jour St. Petersburg Math. J.
\yr 1999
\vol 10
\issue 4
\pages 579--601


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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., Suslina T.A., “The periodic Dirac operator is absolutely continuous”, Integral Equations and Operator Theory, 34:4 (1999), 377–395  crossref  mathscinet  zmath  isi  scopus
    2. Sobolev A.V., “Absolute continuity of the periodic magnetic Schrodinger operator”, Inventiones Mathematicae, 137:1 (1999), 85–112  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Birman M.S., Suslina T.A., “Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum”, Mathematical Results in Quantum Mechanics, Operator Theory : Advances and Applications, 108, 1999, 13–31  mathscinet  zmath  adsnasa  isi
    4. Kuchment P., Levendorskii S., “On absolute continuity of spectra of periodic elliptic operators”, Mathematical Results in Quantum Mechanics, Operator Theory : Advances and Applications, 108, 1999, 291–297  mathscinet  zmath  adsnasa  isi
    5. L. I. Danilov, “Spectrum of the periodic Dirac operator”, Theoret. and Math. Phys., 124:1 (2000), 859–871  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Karpeshina Yu.E., “On the density of states for the periodic Schrodinger operator”, Ark. Mat., 38:1 (2000), 111–137  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Shen Zhongwei, “Absolute continuity of periodic Schrodinger operators with potentials in the Kato class”, Illinois J. Math., 45:3 (2001), 873–893  mathscinet  zmath  isi
    8. Kuchment P., Levendorskii S., “On the structure of spectra of periodic elliptic operators”, Trans. Amer. Math. Soc., 354:2 (2001), 537–569  crossref  mathscinet  isi  scopus
    9. Shen Z.W., “On absolute continuity of the periodic Schrodinger operators”, International Mathematics Research Notices, 2001, no. 1, 1–31  crossref  mathscinet  zmath  isi
    10. 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
    11. Shen Zhongwei, “The periodic Schrodinger operators with potentials in the Morrey class”, J. Funct. Anal., 193:2 (2002), 314–345  crossref  mathscinet  zmath  isi  scopus
    12. L. I. Danilov, “O spektre dvumernykh periodicheskikh operatorov Shredingera i Diraka”, Izv. IMI UdGU, 2002, no. 3(26), 3–98  mathnet
    13. 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
    14. 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
    15. L. I. Danilov, “Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator”, Math. Notes, 73:1 (2003), 46–57  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. 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
    17. Shargorodsky E., Sobolev A., “Quasiconformal mappings and periodic spectral problems in dimension two”, J. Anal. Math., 91 (2003), 67–103  crossref  mathscinet  zmath  isi  scopus
    18. 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
    19. 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
    20. Geyler V.A., Šťovíček P., “Zero modes in a system of Aharonov-Bohm fluxes”, Rev. Math. Phys., 16:7 (2004), 851–907  crossref  mathscinet  zmath  adsnasa  isi  scopus
    21. Karpeshina Yu., “Spectral properties of the periodic magnetic Schrodinger operator in the high-energy region. Two-dimensional case”, Comm. Math. Phys., 251:3 (2004), 473–514  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. 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
    23. 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
    24. 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
    25. 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
    26. 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
    27. 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
    28. 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
    29. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera”, Izv. IMI UdGU, 2013, no. 1(41), 78–95  mathnet
    30. 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
    31. Seo I., “On absolute continuity of the spectrum of periodic Schrödinger operators”, Mon.heft. Math., 180:4 (2016), 893–912  crossref  mathscinet  zmath  isi  scopus
    32. Krupchyk K., Uhlmann G., “Absolute continuity of the periodic Schrödinger operator in transversal geometry”, J. Eur. Math. Soc., 19:2 (2017), 531–550  crossref  mathscinet  zmath  isi  scopus
    33. 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
    34. 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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