Geodesic
On Fourier integral operators
Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 293-334 
V. G. Danilov; Le Vu An'. On Fourier integral operators. Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 293-334. http://geodesic.mathdoc.fr/item/SM_1981_38_3_a0/
@article{SM_1981_38_3_a0,
     author = {V. G. Danilov and Le Vu An'},
     title = {On {Fourier} integral operators},
     journal = {Sbornik. Mathematics},
     pages = {293--334},
     year = {1981},
     volume = {38},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_3_a0/}
}
TY  - JOUR
AU  - V. G. Danilov
AU  - Le Vu An'
TI  - On Fourier integral operators
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 293
EP  - 334
VL  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1981_38_3_a0/
LA  - en
ID  - SM_1981_38_3_a0
ER  - 
%0 Journal Article
%A V. G. Danilov
%A Le Vu An'
%T On Fourier integral operators
%J Sbornik. Mathematics
%D 1981
%P 293-334
%V 38
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1981_38_3_a0/
%G en
%F SM_1981_38_3_a0

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

On the basis of the stationary phase method for oscillatory integrals with complex phase function, the authors prove the coincidence of Fourier integral operators and Maslov's canonical operator. Bibliography: 17 titles.

[1] V. P. Maslov, Operatornye metody, izd-vo “Nauka”, Moskva, 1973 | MR

[2] L. Khërmander, “Integralnye operatory Fure”, Matematika, 16:1 (1972), 17–61 | Zbl

[3] V. P. Maslov, Operational Methods, Mir Publisher, Moscow, 1976 | MR | Zbl

[4] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Moskva, 1965

[5] V. G. Danilov, V. P. Maslov, “Kvaziobraschenie v teorii psevdodifferentsialnykh uravnenii”, Sovremennye problemy matematiki. Itogi nauki i tekhniki, 6, VINITI, Moskva, 1976, 5–132 | MR

[6] J. J. Duistermaat, L. Hörmander, “Fourier integral operators. II”, Acta Math., 128 (1972), 183–269 | DOI | MR | Zbl

[7] A. Melin, J. Sjostrand, “Fourier integral operators with complex-valued phase functions”, Lecture Notes Math., 459 (1975), 121–223 | MR

[8] V. G. Danilov, Ob ogranichennosti psevdodifferentsialnykh operatorov v prostranstvakh Soboleva, Dep. VINITI, No 1383-74; Р. Ж. Математика, 1974, No 10

[9] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, izd-vo “Nauka”, Moskva, 1976 | MR

[10] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, vyp. 1, Fizmatgiz, Moskva, 1966

[11] V. I. Arnold, “Integraly bystro ostsilliruyuschikh funktsii i osobennosti proektsii lagranzhevykh mnogoobrazii”, Funkts. analiz, 6:3 (1972), 61–62 | MR | Zbl

[12] V. V. Kucherenko, “Uravnenie Gamiltona–Yakobi v kompleksnoi neanaliticheskoi situatsii”, DAN SSSR, 213:5 (1973), 1021–1024 | Zbl

[13] V. V. Kucherenko, “Kanonicheskii operator Maslova na rostke kompleksnogo pochti analiticheskogo mnogoobraziya”, DAN SSSR, 213:6 (1973), 1251–1254 | Zbl

[14] B. Yu. Sternin, V. E. Shatalov, “Gladkaya teoriya kanonicheskogo operatora Maslova na kompleksnom lagranzhevom rostke”, Uspekhi matem. nauk, XXIX:3(177) (1974), 229–230 | MR | Zbl

[15] A. S. Mischenko, B. Yu. Sternin, V. E. Shatalov, Metod kanonicheskogo operatora Maslova (kompleksnaya teoriya), izd-vo MIEM, Moskva, 1974

[16] A. G. Prudkovskii, “Metod statsionarnoi fazy v primenenii k integralam, zavisyaschim ot parametra (neanaliticheskii sluchai)”, ZhVMF, 14:2 (1974), 299–311 | MR | Zbl

[17] V. G. Danilov, “Otsenki dlya kanonicheskogo psevdodifferentsialnogo operatora s kompleksnoi fazoi”, DAN SSSR, 244:4 (1979), 800–804 | MR | Zbl