Geodesic
On the solvability of the first Cousin problem for a class of multivalued analytic functions
Izvestiya. Mathematics, Tome 35 (1990) no. 2, pp. 393-409 
B. Yu. Sternin; V. E. Shatalov. On the solvability of the first Cousin problem for a class of multivalued analytic functions. Izvestiya. Mathematics, Tome 35 (1990) no. 2, pp. 393-409. http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The construction, by Maslov's method, of global asymptotics of solutions of differential equations on complex analytic manifolds leads to the first Cousin problem for a certain special class of multivalued analytic functions. This problem (having independent interest) is solved in the present paper. Bibliography: 9 titles.

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

[2] Sternin B. Yu., Shatalov V. E., “O nekotorom integralnom preobrazovanii kompleksnykh analiticheskikh funktsii”, Izv. AN SSSR. Ser. matem., 50:5 (1986), 1054–1076 | MR | Zbl

[3] Sternin B. Yu., Shatalov V. E., “Osobennosti differentsialnykh uravnenii na kompleksno-analiticheskikh mnogoobraziyakh”, Dokl. AN SSSR, 292:5 (1987), 1058–1062 | MR | Zbl

[4] Sternin B. Yu., Shatalov V. E., “Integralnye operatory Laplasa–Radona i osobennosti reshenii differentsialnykh uravnenii na kompleksnykh mnogoobraziyakh”, Globalnyi analiz i matematicheskaya fizika, Voronezh. gos. un-t, Voronezh, 1987, 122–141 | MR

[5] Sternin B. Yu., Shatalov V. E., “Asimptoticheskie razlozheniya reshenii differentsialnykh uravnenii na kompleksnykh mnogoobraziyakh”, Dokl. AN SSSR, 295:1 (1987), 38–41 | Zbl

[6] Khenkin G. M., “Metod integralnykh predstavlenii v kompleksnom analize”, Sovremennye problemy matematiki. Fundamentalnye napravleniya (Itogi nauki i tekhniki), 7, 1985, 23–124 | MR | Zbl

[7] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR

[8] Iosida K., Funktsionalnyi analiz, Mir, M., 1967 | MR

[9] Ganning R., Rossi X., Analiticheskie funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1969 | MR