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TMF, 1995, Volume 103, Number 1, Pages 3–22 (Mi tmf1282)  

This article is cited in 13 scientific papers (total in 13 papers)

Resolvent estimates and the spectrum of the Dirac operator with periodical potential

L. I. Danilov

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

Abstract: Some estimates of the norm of resolvent of Dirac operator on $n$-dimensional tores ($n\ge 2$) for complex values of quasimomentum are given. The absolutely continuity of the spectrum of periodical Dirac operator with potential $V\in L_{\mathrm {\mathrm {loc}}}^\beta (\mathbb R^3)$, $\beta >3$, is proved.

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English version:
Theoretical and Mathematical Physics, 1995, 103:1, 349–365

Bibliographic databases:

Received: 10.03.1994

Citation: L. I. Danilov, “Resolvent estimates and the spectrum of the Dirac operator with periodical potential”, TMF, 103:1 (1995), 3–22; Theoret. and Math. Phys., 103:1 (1995), 349–365

Citation in format AMSBIB
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\by L.~I.~Danilov
\paper Resolvent estimates and the spectrum of the Dirac operator with periodical potential
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\yr 1995
\vol 103
\issue 1
\pages 3--22
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1470934}
\zmath{https://zbmath.org/?q=an:0855.35105}
\transl
\jour Theoret. and Math. Phys.
\yr 1995
\vol 103
\issue 1
\pages 349--365
\crossref{https://doi.org/10.1007/BF02069779}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ96200001}


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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, “On the spectrum of the two-dimensional periodic Dirac operator”, Theoret. and Math. Phys., 118:1 (1999), 1–11  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. L. I. Danilov, “Spectrum of the periodic Dirac operator”, Theoret. and Math. Phys., 124:1 (2000), 859–871  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Kuchment, P, “On the structure of spectra of periodic elliptic operators”, Transactions of the American Mathematical Society, 354:2 (2001), 537  crossref  mathscinet  isi
    4. L. I. Danilov, “O spektre dvumernykh periodicheskikh operatorov Shredingera i Diraka”, Izv. IMI UdGU, 2002, no. 3(26), 3–98  mathnet
    5. 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
    6. 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
    7. 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
    8. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    9. Shen, ZW, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Transactions of the American Mathematical Society, 360:4 (2008), 1741  crossref  mathscinet  zmath  isi
    10. L. I. Danilov, “Absolyutnaya nepreryvnost spektra mnogomernogo periodicheskogo magnitnogo operatora Diraka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 61–96  mathnet
    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  isi
    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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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