On the spectra of finite-dimensional quadratic Bose operators
Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 835-854.

Voir la notice de l'article provenant de la source Math-Net.Ru

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied.
@article{MZM_1997_61_6_a4,
     author = {V. V. Kucherenko and V. P. Maslov},
     title = {On the spectra of finite-dimensional quadratic {Bose} operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {835--854},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a4/}
}
TY  - JOUR
AU  - V. V. Kucherenko
AU  - V. P. Maslov
TI  - On the spectra of finite-dimensional quadratic Bose operators
JO  - Matematičeskie zametki
PY  - 1997
SP  - 835
EP  - 854
VL  - 61
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a4/
LA  - ru
ID  - MZM_1997_61_6_a4
ER  - 
%0 Journal Article
%A V. V. Kucherenko
%A V. P. Maslov
%T On the spectra of finite-dimensional quadratic Bose operators
%J Matematičeskie zametki
%D 1997
%P 835-854
%V 61
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a4/
%G ru
%F MZM_1997_61_6_a4
V. V. Kucherenko; V. P. Maslov. On the spectra of finite-dimensional quadratic Bose operators. Matematičeskie zametki, Tome 61 (1997) no. 6, pp. 835-854. http://geodesic.mathdoc.fr/item/MZM_1997_61_6_a4/

[1] Berezin F. A., Metod vtorichnogo kvantovaniya, Nauka, M., 1965

[2] Bogolyubov N. N., Bogolyubov N. N. (ml.), Vvedenie v kvantovuyu statisticheskuyu mekhaniku, Nauka, M., 1984

[3] Ring P., Schuck P., The nuclear many-body problem, Springer-Verlag, Berlin, 1980

[4] Kucherenko V. V., Maslov V. P., “Privedenie kvadratichnogo bozevskogo operatora k normalnoi forme”, Dokl. RAN, 350:2 (1996), 162–165 | MR

[5] Kucherenko V. V., Maslov V. P., “Normalnye formy kvadratichnykh bozevskikh operatorov”, Matem. zametki, 61:1 (1997), 69–90 | MR | Zbl

[6] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989

[7] Bryuno A. D., Ogranichennaya zadacha trekh tel, Nauka, M., 1990 | Zbl

[8] Kucherenko V. V., The spectral asymptotics of the $N$-particle Schrödinger equation when $N\to\infty$ and the normal forms of quadratic boson operator, Reporte interno No 210, Centro de Investigación y de Estudios Avanzados del IPN, México, 1997

[9] Riez F., Nagy B. Sz., Functional Analysis, Dover Publ., New York, 1990

[10] Kucherenko V. V., “Parametriks dlya uravnenii s vyrozhdayuschimsya simvolom”, Dokl. AN SSSR, 229:4 (1976), 797–800 | MR | Zbl

[11] Yosida K., Functional Analysis, Springer-Verlag, Berlin, 1965

[12] Maslov V. P., Asimptoticheskie metody i teoriya vozmuschenii, Nauka, M., 1988

[13] Kucherenko V. V., “Asimptoticheskie resheniya uravnenii s kompleksnymi kharakteristikami”, Matem. sb., 95:2 (1974), 163–213 | MR | Zbl

[14] Kucherenko V. V., “Asimptotika resheniya zadachi Koshi dlya uravnenii s kompleksnymi kharakteristikami”, Itogi nauki i tekhn. Sovrem. probl. matem., 8, VINITI, M., 1977, 41–137 | Zbl

[15] Maslov V. P., Operatornye metody, Nauka, M., 1973

[16] Kucherenko V. V., Motylëv Yu. L., “O granitsakh primenimosti metoda kanonicheskogo operatora Maslova dlya uravnenii s negladkimi kharakteristicheskimi kornyami”, Izv. AN SSSR. Ser. matem., 50:4 (1986), 741–762 | MR