Geodesic
Poisson symmetry algebras and the asymptotics of spectral series
Funkcionalʹnyj analiz i ego priloženiâ, Tome 20 (1986) no. 1, pp. 21-32.

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

@article{FAA_1986_20_1_a2,
     author = {M. V. Karasev},
     title = {Poisson symmetry algebras and the asymptotics of spectral series},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_1986_20_1_a2/}
}
TY  - JOUR
AU  - M. V. Karasev
TI  - Poisson symmetry algebras and the asymptotics of spectral series
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 1986
SP  - 21
EP  - 32
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_1986_20_1_a2/
LA  - ru
ID  - FAA_1986_20_1_a2
ER  - 
%0 Journal Article
%A M. V. Karasev
%T Poisson symmetry algebras and the asymptotics of spectral series
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 1986
%P 21-32
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_1986_20_1_a2/
%G ru
%F FAA_1986_20_1_a2
M. V. Karasev. Poisson symmetry algebras and the asymptotics of spectral series. Funkcionalʹnyj analiz i ego priloženiâ, Tome 20 (1986) no. 1, pp. 21-32. http://geodesic.mathdoc.fr/item/FAA_1986_20_1_a2/

[1] Maslov V.P., Teoriya vozmuschenii i asimptoticheskie metody, Izd. MGU, M., 1965

[2] Mischenko A.S., Sternin B.Yu., Shatalov V.E., Lagranzhevy mnogoobraziya i metod kanonicheskogo operatora, Nauka, M., 1978 | MR

[3] Weinstein A., “Asymptotics of the eigenvalues clusters for the laplacian plus a potential”, Duke Math. J., 44 (1977), 883–892 | DOI | MR | Zbl

[4] Colin de Verdiere Y., “Sur le spectre des operateurs elliptiques a bicaracteristiques toutes periodiques”, Comm. Math. Helv., 54:3 (1979), 508–522 | MR | Zbl

[5] Guillemin F., Sternberg S., “Some problems in integral geometry and some related problems in microlocal analysis”, Amer. J. Math., 101 (1979), 915–955 | DOI | MR | Zbl

[6] Marsden J., Ratiu T., Weinstein A., “Semi-direct products and reduction in mechanics”, Trans. Amer. Math. Soc., 281, no. 1, 1984, 147–177 | DOI | MR | Zbl

[7] Karasev M.B., “Asimptotika sobstvennykh znachenii operatorov s puassonovskoi algebroi simmetrii u starshego simvola”, Funktsion. analiz i ego pril., 18:2 (1984), 65–66 | MR | Zbl

[8] Maslov V.P., “Primenenie metoda uporyadochennykh operatorov dlya polucheniya tochnykh reshenii”, TMF, 33:2 (1977), 185–209 | MR | Zbl

[9] Karasev M.V., “Asimptoticheskii spektr i front ostsillyatsii dlya operatorov s nelineinymi kommutatsionnymi sootnosheniyami”, DAN SSSR, 243:1 (1978), 15–18 | MR | Zbl

[10] Kirillov A.A., “Lokalnye algebry Li”, UMN, 31:4 (1976), 57–76 | MR | Zbl

[11] Faddeev L.D., “Kvantovye vpolne integriruemye modeli teorii polya”, Problemy kvantovoi teorii polya, Izd. OIYaI, Dubna, 1979

[12] Sklyanin E.K., “O nekotorykh algebraicheskikh strukturakh, svyazannykh s uravneniyami Yanga–Bakstera”, Funktsion. analiz i ego pril., 16:4 (1982), 27–34 | MR | Zbl

[13] Karasev M.V., Maslov V.P., “Algebry s obschimi perestanovochnymi sootnosheniyami i ikh primeneniya”, Sovr. problemy mat., 13, 1979, 145–267 | MR | Zbl

[14] Karasev M.V., Maslov V.P., “Globalnye operatory regulyarnogo predstavleniya”, DAN SSSR, 257:1 (1981), 33–38 | MR | Zbl

[15] Karasev M.V., Usloviya kvantovaniya Maslova v vysshikh kogomologiyakh i analogi ob'ektov teorii Li dlya kanonicheskikh rassloenii simplekticheskikh mnogoobrazii, Dep. VINITI, Dep. No 1092-82; No 1093-82, MIEM, M., 1981

[16] Karasev M.V., Maslov V.P., “Asimptoticheskoe i geometricheskoe kvantovanie”, UMN, 39:6 (1984), 115–173 | MR | Zbl

[17] Lere Zh., Lagranzhev analiz i kvantovaya mekhanika, Mir, M., 1981 | MR

[18] Maslov V.P., Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR

[19] Karasev M.V., Maslov V.P., “Psevdodifferentsialnye operatory i kanonicheskii operator v obschikh simplekticheskikh mnogoobraziyakh”, Izv. AN SSSR, ser. mat., 47:5 (1983), 999–1029 | MR | Zbl

[20] Weinstein A., “The local structure of Poisson manifolds”, J. Diff. Geom., 18:3 (1983), 523–557 | MR | Zbl

[21] Nekhoroshev H.H., “Peremennye deistvie–ugol i ikh obobschenie”, Trudy MMO, 26, 1972, 181–198 | Zbl

[22] Karasev M.V., “Asimptotika spektra smeshannykh sostoyanii dlya uravnenii samosoglasovannogo polya”, TMF, 61:1 (1984), 118–127 | MR | Zbl

[23] Arnold V.I., “O kharakteristicheskom klasse, vkhodyaschem v usloviya kvantovaniya”, Funktsion. analiz i ego pril., 1:1 (1967), 1–14 | MR

[24] Hess H., “On a geometric quantization scheme generalizing those of Kostant–Souriau and Czyz.”, Lect. Notes Phys., 139 (1981), 1–35 | DOI | MR

[25] Kirillov A.A., Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[26] Dobrokhotov S.Yu., Maslov V.P., “Nekotorye prilozheniya teorii kompleksnogo rostka k uravneniyam s malym parametrom”, Sovr. problemy mat., 5, 1975, 141–211 | MR | Zbl

[27] Vorobev Yu.M., Dobrokhotov S.Yu., “Kvaziklassicheskie asimptotiki dlya diskretnykh modelei elektron-fotonnogo vzaimodeistviya: metod Maslova i adiabaticheskoe priblizhenie”, TMF, 57:1 (1983), 63–74 | MR

[28] Maslov V.P., Danilov V.G., “Printsip dvoistvennosti Pontryagina dlya vychisleniya effekta tipa Cherepkova v kristallakh i raznostnykh skhemakh”, Trudy MIAN 1983, 166, 130–160 | MR | Zbl

[29] Novikov S.P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | DOI | MR | Zbl

[30] Karasev M.V., Kvantovanie nelineinykh skobok Li–Puassona v kvaziklassicheskom priblizhenii, Preprint ITF AN USSR. ITF-85-72R, Kiev, 1985