A direct method of solving the singular integral equation with the Hilbert kernel
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 65-70
Cet article a éte moissonné depuis la source Math-Net.Ru
In this paper we consider a class of singular integral second-kind equations with Hilbert kernel on the unit circumference. We theoretically justify a method based on an interpolation-type operator.
Mots-clés :
Lebesgue space, convergence
Keywords: integral equation, singular integral with the Hilbert kernel, error estimate.
Keywords: integral equation, singular integral with the Hilbert kernel, error estimate.
@article{IVM_2009_6_a8,
author = {V. P. Kadushin and A. I. Shakirov},
title = {A direct method of solving the singular integral equation with the {Hilbert} kernel},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {65--70},
year = {2009},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2009_6_a8/}
}
TY - JOUR AU - V. P. Kadushin AU - A. I. Shakirov TI - A direct method of solving the singular integral equation with the Hilbert kernel JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2009 SP - 65 EP - 70 IS - 6 UR - http://geodesic.mathdoc.fr/item/IVM_2009_6_a8/ LA - ru ID - IVM_2009_6_a8 ER -
V. P. Kadushin; A. I. Shakirov. A direct method of solving the singular integral equation with the Hilbert kernel. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 65-70. http://geodesic.mathdoc.fr/item/IVM_2009_6_a8/
[1] Ermolaeva L. B., Approksimativnye svoistva polinomialnykh operatorov i reshenie integralnykh i integro-differentsialnykh uravnenii metodom podoblastei, Dis. $\dots$ kand. fiz.-matem. nauk, Kazan, 1987 | Zbl
[2] Gabdulkhaev B. G., Optimalnye approksimatsii reshenii lineinykh zadach, Izd-vo Kazansk. un-ta, Kazan, 1980, 232 pp. | MR
[3] Gabdulkhaev B. G., Chislennyi analiz singulyarnykh integralnykh uravnenii. Izbrannye glavy, Izd-vo Kazansk. un-ta, Kazan, 1995, 230 pp. | MR
[4] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977, 640 pp. | MR | Zbl
[5] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968, 512 pp. | MR | Zbl
[6] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977, 742 pp. | MR