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TMF, 1999, Volume 118, Number 1, Pages 3–14 (Mi tmf682)  

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

On the spectrum of the two-dimensional periodic Dirac operator

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We prove the absolute continuity of the Dirac operator spectrum in $\mathbf R^2$ with the scalar potential $V$ and the vector potential $A=(A_1,A_2)$ being periodic functions $($with a common period lattice$)$ such that $V,A_j\in L^q_{\operatorname{loc}}(\mathbf R^2)$, $q>2$.

DOI: https://doi.org/10.4213/tmf682

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English version:
Theoretical and Mathematical Physics, 1999, 118:1, 1–11

Bibliographic databases:

Received: 25.06.1998

Citation: L. I. Danilov, “On the spectrum of the two-dimensional periodic Dirac operator”, TMF, 118:1 (1999), 3–14; Theoret. and Math. Phys., 118:1 (1999), 1–11

Citation in format AMSBIB
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\by L.~I.~Danilov
\paper On the spectrum of the two-dimensional periodic Dirac operator
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\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 1
\pages 1--11
\crossref{https://doi.org/10.1007/BF02557191}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. I. Danilov, “Spectrum of the periodic Dirac operator”, Theoret. and Math. Phys., 124:1 (2000), 859–871  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Kuchment, P, “On the structure of spectra of periodic elliptic operators”, Transactions of the American Mathematical Society, 354:2 (2001), 537  crossref  mathscinet  isi  scopus  scopus  scopus
    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, “Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator”, Math. Notes, 73:1 (2003), 46–57  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. 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
    6. Richard, S, “On perturbations of Dirac operators with variable magnetic field of constant direction”, Journal of Mathematical Physics, 45:11 (2004), 4164  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. 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
    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. Richard, S, “On the spectrum of magnetic Dirac operators with Coulomb-type perturbations”, Journal of Functional Analysis, 250:2 (2007), 625  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. 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  scopus  scopus
    12. L. I. Danilov, “O spektre periodicheskogo magnitnogo operatora Diraka”, Izv. IMI UdGU, 2016, no. 2(48), 3–21  mathnet  elib
    13. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    14. L. I. Danilov, “O spektre relyativistskogo gamiltoniana Landau s periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 54 (2019), 3–26  mathnet  crossref  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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