Optimal quadrature and cubature formulas for singular integrals with Hilbert kernels
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2004), pp. 16-27.

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L. A. Apaicheva. Optimal quadrature and cubature formulas for singular integrals with Hilbert kernels. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2004), pp. 16-27. http://geodesic.mathdoc.fr/item/IVM_2004_4_a2/

[1] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Fizmatgiz, M., 1968, 512 pp. | MR

[2] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977, 640 pp. | MR | Zbl

[3] Gabdulkhaev B. G., “Konechnomernye approksimatsii singulyarnykh integralov i pryamye metody resheniya osobykh integralnykh i integro-differentsialnykh uravnenii”, Itogi nauki i tekhn. Matem. analiz, 18, VINITI, M., 1980, 251–307 | MR

[4] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo Kazansk. un-ta, Kazan, 1980, 232 pp. | MR

[5] Tikhonenko N. Ya., Priblizhennoe reshenie kraevykh zadach teorii analiticheskikh funktsii i ikh prilozheniya, Dis. ... dokt. fiz.-matem. nauk, Kiev, 1994, 327 pp. | Zbl

[6] Apaicheva L. A., Priblizhennoe vychislenie singulyarnykh integralov v klasse funktsii $W^rH_k[\varphi]$, Dep. v VINITI 19.12.85, No 8722-B, Kazansk. khim.-tekhnol. in-t, Kazan, 1985, 40 pp.

[7] Stechkin S. B., “O poryadke nailuchshikh priblizhenii nepreryvnykh funktsii”, Izv. AN SSSR. Ser. matem., 15:3 (1951), 219–242 | Zbl

[8] Stechkin S. B., “O nailuchshem priblizhenii sopryazhennykh funktsii trigonometricheskimi polinomami”, Izv. AN SSSR. Ser. matem., 20:2 (1956), 197–206 | Zbl

[9] Bari N. K., “O nailuchshem priblizhenii trigonometricheskimi polinomami dvukh sopryazhennykh funktsii”, Izv. AN SSSR. Ser. matem., 19:5 (1955), 285–302 | MR | Zbl

[10] Lozinskii S. M., “Obraschenie teorem Dzheksona”, DAN SSSR, 83:5 (1952), 645–648 | MR

[11] Zygmund A., “Smooth functions”, Duke Math. J., 12:1 (1945), 47–76 | DOI | MR | Zbl

[12] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961, 936 pp. | MR

[13] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Fizmatgiz, M., 1960, 624 pp.

[14] Stepanets A. I., Ravnomernye priblizheniya trigonometricheskimi polinomami, Nauk. dumka, Kiev, 1981, 340 pp. | MR | Zbl

[15] Daugavet I. K., Vvedenie v teoriyu priblizheniya funktsii, Izd-vo LGU, L., 1977, 184 pp. | MR | Zbl

[16] Velev G. D., O priblizhennykh metodakh vychisleniya singulyarnykh integralov, Dis. ... kand. fiz.-matem. nauk, Kazan, 1982, 162 pp.

[17] Stechkin S. B., “Metody summirovaniya S. N. Bernshteina–V. Rogozinskogo”, Khardi G. Kh., Raskhodyaschiesya ryady, In. lit., M., 1951, 479–492

[18] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977, 490 pp. | MR | Zbl

[19] Musaev B. I., Salaev V. V., “O skhodimosti kvadraturnykh protsessov dlya singulyarnogo integrala s yadrom Gilberta”, Sovremen. probl. teorii funktsii, Materialy Vses. shkoly po teorii funktsii (Baku, 1977), 1980, 186–194

[20] Feschiev I. Kh., “K priblizhennomu vychisleniyu singulyarnykh integralov”, Dokl. Bolg. AN., 30:8 (1977), 1109–1112 | MR | Zbl

[21] Gabdulkhaev B. G., “Kubaturnye formuly dlya singulyarnykh integralov. I”, Izv. Matem. in-ta Bolg. AN, 11 (1970), 181–196 | Zbl

[22] Gabdulkhaev B. G., “Kubaturnye formuly dlya singulyarnykh integralov. II”, Izv. vuzov. Matematika, 1975, no. 4, 3–13 | Zbl

[23] Apaicheva L. A., Velev G. D., “O nekotorykh kvadraturnykh i kubaturnykh formulakh dlya singulyarnykh integralov”, Izv. vuzov. Matematika, 1976, no. 3, 3–12

[24] Gabdulkhaev B. G., Sharipov R. N., “Optimizatsiya kvadraturnykh formul s kratnymi uzlami dlya singulyarnykh integralov”, Izv. vuzov. Matematika, 1979, no. 12, 62–66 | MR | Zbl

[25] Gabdulkhaev B. G., “Ekstremalnye zadachi teorii singulyarnykh kubatur”, Vsesoyuzn. shkola po teorii funktsii, posvyasch. 100-letiyu so dnya rozhd. N. N. Luzina, Tez. dokl., Kemerovo, 1983, 29