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

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Teoreticheskaya i Matematicheskaya Fizika, 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

Full-text PDF (1617 kB) Citations (13)

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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.

Received: 10.03.1994

English version:
Theoretical and Mathematical Physics, 1995, Volume 103, Issue 1, Pages 349–365
DOI: https://doi.org/10.1007/BF02069779

Bibliographic databases:

Language: Russian

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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\jour Theoret. and Math. Phys.

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\crossref{https://doi.org/10.1007/BF02069779}

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Linking options:

https://www.mathnet.ru/eng/tmf1282

https://www.mathnet.ru/eng/tmf/v103/i1/p3

This publication is cited in the following 13 articles:

L. I. Danilov, “O spektre periodicheskogo magnitnogo operatora Diraka”, Izv. IMI UdGU, 2016, no. 2(48), 3–21
Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414
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
Shen, ZW, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Transactions of the American Mathematical Society, 360:4 (2008), 1741
L. I. Danilov, “Absolyutnaya nepreryvnost spektra mnogomernogo periodicheskogo magnitnogo operatora Diraka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 61–96
L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76
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
L. I. Danilov, “Ob otsutstvii sobstvennykh znachenii v spektre dvumernykh periodicheskikh operatorov Diraka i Shredingera”, Izv. IMI UdGU, 2004, no. 1(29), 49–84
L. I. Danilov, “Absolute Continuity of the Spectrum of a Periodic Schrödinger Operator”, Math. Notes, 73:1 (2003), 46–57
L. I. Danilov, “O spektre dvumernykh periodicheskikh operatorov Shredingera i Diraka”, Izv. IMI UdGU, 2002, no. 3(26), 3–98
Kuchment, P, “On the structure of spectra of periodic elliptic operators”, Transactions of the American Mathematical Society, 354:2 (2001), 537
L. I. Danilov, “Spectrum of the periodic Dirac operator”, Theoret. and Math. Phys., 124:1 (2000), 859–871
L. I. Danilov, “On the spectrum of the two-dimensional periodic Dirac operator”, Theoret. and Math. Phys., 118:1 (1999), 1–11

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	449
Full-text PDF :	141
References:	84
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