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Izv. IMI UdGU, 2004, Issue 1(29), Pages 49–84 (Mi iimi235)  

This article is cited in 8 scientific papers (total in 8 papers)

On absence of eigenvalues in the spectra of two-dimensional periodic Dirac and Schrödinger operators

L. I. Danilov

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

Abstract: We prove the absence of eigenvalues in the spectrum of two-dimensional periodic Dirac operator with martix coefficients of the class $L^{\infty}$ and strongly subordinate matrix potential. We also obtain conditions for the absence of eigenvalues in the spectrum of two-dimensional periodic Schrödinger operator with variable metric.

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UDC: 517.958+517.984.5

Citation: L. I. Danilov, “On absence of eigenvalues in the spectra of two-dimensional periodic Dirac and Schrödinger operators”, Izv. IMI UdGU, 2004, no. 1(29), 49–84

Citation in format AMSBIB
\Bibitem{Dan04}
\by L.~I.~Danilov
\paper On absence of eigenvalues in the spectra of two-dimensional periodic Dirac and Schr\"odinger operators
\jour Izv. IMI UdGU
\yr 2004
\issue 1(29)
\pages 49--84
\mathnet{http://mi.mathnet.ru/iimi235}


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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, “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
    2. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    3. 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
    4. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera”, Izv. IMI UdGU, 2013, no. 1(41), 78–95  mathnet
    5. 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
    6. 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
    7. L. I. Danilov, “O spektre relyativistskogo gamiltoniana Landau s periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 54 (2019), 3–26  mathnet  crossref
    8. L. I. Danilov, “Spectrum of the Landau Hamiltonian with a periodic electric potential”, Theoret. and Math. Phys., 202:1 (2020), 41–57  mathnet  crossref
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