Geodesic
Resolvent estimates and the spectrum of the Dirac operator with periodical potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 1, pp. 3-22 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{TMF_1995_103_1_a0,
     author = {L. I. Danilov},
     title = {Resolvent estimates and the spectrum of the {Dirac} operator with periodical potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--22},
     year = {1995},
     volume = {103},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_1_a0/}
}
TY  - JOUR
AU  - L. I. Danilov
TI  - Resolvent estimates and the spectrum of the Dirac operator with periodical potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 3
EP  - 22
VL  - 103
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_103_1_a0/
LA  - ru
ID  - TMF_1995_103_1_a0
ER  - 
%0 Journal Article
%A L. I. Danilov
%T Resolvent estimates and the spectrum of the Dirac operator with periodical potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 3-22
%V 103
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1995_103_1_a0/
%G ru
%F TMF_1995_103_1_a0
L. I. Danilov. Resolvent estimates and the spectrum of the Dirac operator with periodical potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 1, pp. 3-22. http://geodesic.mathdoc.fr/item/TMF_1995_103_1_a0/

[1] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 2, Mir, M., 1978 | MR

[2] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 4, Mir, M., 1982 | MR

[3] Gelfand I. M., DAN SSSR, 73:6 (1950), 1117–1120 | MR | Zbl

[4] Danilov L. I., TMF, 85:1 (1990), 41–53 | MR | Zbl

[5] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki, T. 1, Mir, M., 1977 | MR

[6] Thomas L. E., Commun. Math. Phys., 33 (1973), 335–343 | DOI | MR

[7] Danilov L. I., Spektr operatora Diraka s periodicheskim potentsialom, III, Dep. v VINITI 10.07.92. No 2252-V92, VINITI, M., 1992

[8] Danilov L. I., Spektr operatora Diraka s periodicheskim potentsialom, II, Dep. v VINITI 20.02.92. No 586-V92, VINITI, M., 1992

[9] Danilov L. I., Spektr operatora Diraka s periodicheskim potentsialom, I, Dep. v VINITI 12.12.91. No 4588-V91, VINITI, M., 1991

[10] Danilov L. I., O spektre operatora Diraka s periodicheskim potentsialom: Preprint, FTI UrO AN SSSR, Sverdlovsk, 1987

[11] Stein I., Singulyarnye integraly i differenitsialnye svoistva funktsii, Mir, M., 1973 | MR

[12] Chandrasekkharan K., Vvedenie v analiticheskuyu teoriyu chisel, Mir, M., 1974 | MR