Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential
Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 115-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The spectrum of the multidimensional polyharmonic differential operator is investigated. The finiteness of the number of connected components of the spectrum is proved. Bibliography: 10 titles.
@article{SM_1982_41_1_a6,
     author = {M. M. Skriganov},
     title = {Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a~periodic potential},
     journal = {Sbornik. Mathematics},
     pages = {115--125},
     year = {1982},
     volume = {41},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_41_1_a6/}
}
TY  - JOUR
AU  - M. M. Skriganov
TI  - Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential
JO  - Sbornik. Mathematics
PY  - 1982
SP  - 115
EP  - 125
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1982_41_1_a6/
LA  - en
ID  - SM_1982_41_1_a6
ER  - 
%0 Journal Article
%A M. M. Skriganov
%T Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential
%J Sbornik. Mathematics
%D 1982
%P 115-125
%V 41
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1982_41_1_a6/
%G en
%F SM_1982_41_1_a6
M. M. Skriganov. Finiteness of the number of lacunae in the spectrum of the multidimensional polyharmonic operator with a periodic potential. Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 115-125. http://geodesic.mathdoc.fr/item/SM_1982_41_1_a6/

[1] A. Vilson, Kvantovaya teoriya metallov, OGIZ, Moskva–Leningrad, 1941

[2] Dzh. Kalluei, Teoriya energeticheskoi zonnoi struktury, izd-vo “Mir”, Moskva, 1969

[3] I. M. Gelfand, “Razlozhenie po sobstvennym funktsiyam uravneniya s periodicheskimi koeffitsientami”, DAN SSSR, 73:6 (1950), 1117–1120 | MR

[4] M. S. P. Eastham, The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh, 1973 | Zbl

[5] M. Reed, B. Simon, Methodes of Modern Mathematical Psysics, v. 4, Academic Press, New York–London, 1978 | MR | Zbl

[6] M. M. Skriganov, “O gipoteze Bete–Zommerfelda”, DAN SSSR, 244:3 (1979), 553–554 | MR

[7] M. M. Skriganov, “Dokazatelstvo gipotezy Bete–Zommerfelda v razmernosti dva”, DAN SSSR, 248:1 (1979), 39–42 | MR | Zbl

[8] Dzh. V. S. Kassels, Vvedenie v geometriyu chisel, izd-vo “Mir”, Moskva, 1965 | MR

[9] T. Kato, Teoriya vozmuschenii lineinykh operatorov, izd-vo “Mir”, Moskva, 1972

[10] G. G. Khardi, Dzh. E. Littlvud, G. Polia, Neravenstva, IL, Moskva, 1948