Geodesic
On the microlocal structure of pseudodifferential operators
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 515-527 
V. V. Lychagin; B. Yu. Sternin. On the microlocal structure of pseudodifferential operators. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 515-527. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The microlocal structure of pseudodifferential operators is studied in a neighborhood of a degenerate singular point, and the normal forms of the complete symbols are determined. Bibliography: 18 titles.

[1] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1971 | MR

[2] Egorov Yu. V., “Kanonicheskie preobrazovaniya i psevdodifferentsialnye operatory”, Tr. MMO, 24 (1971), 3–28 | MR | Zbl

[3] Lychagin V. V., “Lokalnaya klassifikatsiya nelineinykh differentsialnykh uravnenii v chastnykh proizvodnykh pervogo poryadka”, UMN, 30:1 (1975), 101–171 | MR | Zbl

[4] Lychagin V. V., “O dostatochnykh orbitakh gruppy kontaktnykh diffeomorfizmov”, Matem. sb., 104(146) (1977), 148–270

[5] Lychagin V. V., “Spektralnye posledovatelnosti i normalnye formy algebr Li vektornykh polei”, UMN, 38:5 (1983), 199–200 | MR | Zbl

[6] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[7] Nazaikinskii V. V., Oshmyan V. G., Sternin B. Yu., Shatalov V. E., “Integralnye operatory. Fure i kanonicheskii operator”, UMN, 36:2 (1981), 81–140 | MR | Zbl

[8] Sternin B. Yu., “O mikrolokalnoi strukture differentsialnykh operatorov”, UMN, 6 (32), 235–236 | MR | Zbl

[9] Sternin B. Yu., “Metod kanonicheskogo operatora Maslova”, Kompleksnyi analiz i mnogoobraziya, Kiev, 1978, 47–113 | MR | Zbl

[10] Sternin B. Yu., “O regulyarizatsii uravnenii subglavnogo tipa”, UMN, 37:2 (1982), 235–236 | MR | Zbl

[11] Sternin B. Yu., “O differentsialnykh uravneniyakh subglavnogo tipa”, DAN SSSR, 265:5 (1982), 1078–1081 | MR | Zbl

[12] Sternin B. Yu., “Differentsialnye uravneniya subglavnogo tipa”, Matem. sb., 125(167) (1984), 38–69 | MR

[13] Sternin B. Yu., Shatalov V. E., “Kontaktnaya geometriya i lineinye differentsialnye uravneniya”, Geometriya i topologiya v globalnykh nelineinykh zadachakh, Voronezh, 1984, 92–113 | MR | Zbl

[14] Alinhac S., “On the reduction on pseudo-differential operators to canonical forms”, J. Different. Equat., 31:2 (1979), 165–182 | DOI | MR | Zbl

[15] Guillemin V., Schaeffer D., “On a certain class of Fuchsian partial differential equations.”, Duke Math. J., 44:1 (1977), 157–199 | DOI | MR | Zbl

[16] Daistermaat J. J., Hörmander L., “Fourier integraloperators II”, Acta math., 128 (1972), 183–269 | DOI | MR

[17] Oshima T., “Singularities in contact geometry and degenerate pseudodifferential equations”, J. Fac. Sci. Univ. Tokyo, 1 (1974), 43–83 | MR

[18] Sternin B. Ja., Satalov V. E., “The Contact Geometry and Linear Differential Equations”, Lect. Notes, 1984, no. 1108