Dirichlet problem for holomorphic functions in spaces with determined modulus of continuity
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 107-116 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study and solve the Dirichlet problem for holomorphic functions in spaces with a determined modulus of continuity: the existence of the function which is holomorphic inside a disk is proved by the limit values of its real part on the disk's boundary.
Keywords: Dirichlet problem, holomorphic functions, modulus of continuity.
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A. Yu. Timofeev. Dirichlet problem for holomorphic functions in spaces with determined modulus of continuity. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 107-116. http://geodesic.mathdoc.fr/item/VUU_2011_3_a9/

[1] Ilchukov A. S., Timofeev A. Yu., “Zadacha Dirikhle dlya golomorfnykh funktsii v prostranstvakh, opisyvaemykh povedeniem modulya nepreryvnosti”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2010, no. 1, 58–65

[2] Reissig M., Timofeev A., “Dirichlet problems for generalized Cauchy–Riemann systems with singular coefficients”, Complex variables, 73:1–2 (2005), 653–672 | DOI | MR

[3] Tutschke W., Vorlesungen uber partielle Differentialgleichungen. Klassische, functionalanalytische und komplexe Methoden, Teubner-Texte zur Mathematik, Leipzig, 1978, 193 pp. | MR

[4] Monakhov V. N., Kraevye zadachi so svobodnymi granitsami dlya ellipticheskikh sistem uravnenii, Nauka, Novosibirsk, 1977, 424 pp. | MR

[5] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A., Mikhlin S. G., Rakovschik L. S., Stetsenko V. Ya., Integralnye uravneniya, Nauka, M., 1968, 448 pp.

[6] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M., 1950, 336 pp. | MR

[7] Geronimus Ya. L., “O nekotorykh integralnykh uravneniyakh”, DAN SSSR, 98:1 (1954), 5–7 | MR | Zbl

[8] Tamrazov P. M., “Konturnye i telesnye strukturnye svoistva golomorfnykh funktsii kompleksnogo peremennogo”, Uspekhi matematicheskikh nauk, 28:1(169) (1973), 131–161 | MR | Zbl

[9] Guseinov A. I., Mukhtarov Kh. Sh., Vvedenie v teoriyu nelineinykh singulyarnykh integralnykh uravnenii, Nauka, M., 1980, 416 pp. | MR

[10] Babaev A. A., Salaev V. V., “Ob odnom analoge teoremy Plemelya–Privalova v sluchae negladkikh krivykh i ee prilozheniya”, DAN SSSR, 161:2 (1965), 267–269 | MR

[11] Bari N. K., “O nailuchshem priblizhenii trigonometricheskimi polinomami dvukh sopryazhennykh funktsii”, Izvestiya Akademii nauk SSSR. Ser. Matem., 19:5 (1955), 285–302 | MR | Zbl

[12] Napalkov V. V., Timofeev A. Yu., “Zadacha Dirikhle dlya golomorfnykh funktsii v obobschennykh prostranstvakh Geldera”, Doklady Akademii nauk, 432:3 (2010), 1–3

[13] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Trudy Moskovskogo matem. ob-va, 5, 1956, 485–522 | MR

[14] Michlin S. G., Prössdorf S., Singuläre Integraloperatoren, Akademie-Verlag, Berlin, 1980, 514 pp. | MR | Zbl

[15] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966, 630 pp. | MR | Zbl