Geodesic
On a~class of singular integral operators with kernels of polar-logarithmic type
Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 127-143.

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Integral operators with polar-logarithmic kernels which arise in connection with a problem of F. D. Gahov are studied in the space $L_p(\mathscr L)$. Necessary and sufficient conditions that the operator be Noetherian and a formula for the index of the operators are obtained. A complete solution of Gahov's problem is obtained. Bibliography: 10 titles. 
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N. L. Vasilevskii. On a~class of singular integral operators with kernels of polar-logarithmic type. Izvestiya. Mathematics , Tome 10 (1976) no. 1, pp. 127-143. http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a7/

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

[2] Gakhov F. D., Kraevye zadachi, Fizmatgiz, M., 1963 | MR

[3] Gokhberg I. Ts., Krupnik N. Ya., “Singulyarnye integralnye operatory s kusochno-nepreryvnymi koeffitsientami i ikh simvoly”, Izv. AN SSSR. Ser. matem., 35 (1971), 940–964 | MR | Zbl

[4] Vasilevskii N. L., “Ob usloviyakh neterovosti i formula dlya indeksa odnogo klassa integralnykh operatorov tipa potentsiala”, Dokl. AN SSSR, 202:4 (1972), 747–750 | MR | Zbl

[5] Melnik I. M., Issledovaniya po sovremennym problemam teorii funktsii kompleksnogo peremennogo, Fizmatgiz, M., 1961

[6] Gordadze E. G., “O singulyarnykh integralakh s yadrom Koshi”, Soobsch. AN GruzSSR, 37:3 (1965), 521–526 | MR | Zbl

[7] Kantorovich L. V., “Ob integralnykh operatorakh”, Uspekhi matem. nauk, 11:2(68) (1956), 3–29 | MR | Zbl

[8] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971 | MR

[9] Vasilevskii N. L., “Teoriya Netera odnogo klassa integralnykh operatorov tipa potentsiala”, Izv. VUZov, Matematika, 1974, no. 7, 12–20 | MR | Zbl

[10] Gokhberg I. Ts., Krupnik N. Ya., “Sistemy singulyarnykh integralnykh uravnenii v prostranstvakh $L_p$ s vesom”, Dokl. AN SSSR, 186:5 (1969), 998–1001 | Zbl