Geodesic
A direct method of solving the singular integral equation with the Hilbert kernel
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2009), pp. 65-70.

Voir la notice de l'article provenant de 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. 
@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},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     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
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_6_a8/
LA  - ru
ID  - IVM_2009_6_a8
ER  - 
%0 Journal Article
%A V. P. Kadushin
%A A. I. Shakirov
%T A direct method of solving the singular integral equation with the Hilbert kernel
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 65-70
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_6_a8/
%G ru
%F IVM_2009_6_a8
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