Geodesic
A boundary value problem of linear conjugation in the theory of functions
Izvestiya. Mathematics, Tome 14 (1980) no. 1, pp. 175-192 
A. P. Soldatov. A boundary value problem of linear conjugation in the theory of functions. Izvestiya. Mathematics, Tome 14 (1980) no. 1, pp. 175-192. http://geodesic.mathdoc.fr/item/IM2_1980_14_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The matrix case of a boundary value problem of linear conjugation in the theory of analytic functions, for arbitrary piecewise smooth curves, is treated, as is the corresponding adjoint problem. For these problems Noetherian theorems are proved, a family of canonical functions is constructed, and the behavior of these solutions at corner points of the curve is described. Bibliography: 9 titles.

[1] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | Zbl

[2] Vekua N. P., Sistemy singulyarnykh integralnykh uravnenii, Nauka, M., 1970 | MR | Zbl

[3] Gakhov F. D., “Kraevaya zadacha Rimana dlya sistemy par funktsii”, Uspekhi matem. nauk, 7:4 (1952), 3–54 | MR | Zbl

[4] Khvedelidze B. V., “Lineinye razryvnye granichnye zadachi teorii funktsii, singulyarnye integralnye uravneniya i nekotorye ikh prilozheniya”, Tr. Tbilissk. matem. in-ta AN Gruz. SSR, 23, 1956, 3–158

[5] Soldatov A. P., “K teorii singulyarnykh integralnykh operatorov klassicheskogo tipa”, Differentsialnye uravneniya, 15:3 (1979) | MR

[6] Soldatov A. P., “Kategoriya dvoistvennosti v teorii neterovykh operatorov”, Differentsialnye uravneniya, 15:2 (1979) | MR

[7] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[8] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[9] Soldatov A. P., “K neterovskoi teorii operatorov. Odnomernye singulyarnye integralnye operatory obschego vida”, Differentsialnye uravneniya, 14:4 (1978), 706–718 | MR | Zbl