Geodesic
A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 54-60 
V. S. Pilidi. A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 54-60. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a6/
@article{VMJ_2014_16_4_a6,
     author = {V. S. Pilidi},
     title = {A convergence criterion of a~smoothing method for singular integral operators with piecewise continuous coefficients},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {54--60},
     year = {2014},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a6/}
}
TY  - JOUR
AU  - V. S. Pilidi
TI  - A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 54
EP  - 60
VL  - 16
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a6/
LA  - ru
ID  - VMJ_2014_16_4_a6
ER  - 
%0 Journal Article
%A V. S. Pilidi
%T A convergence criterion of a smoothing method for singular integral operators with piecewise continuous coefficients
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 54-60
%V 16
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a6/
%G ru
%F VMJ_2014_16_4_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

For a complete singular integral operator with piecewise continuous coefficients on the real axis a criterion of convergence of an approximation method by a family of complete singular integral operators with the coefficients being continuous on the one-point compactification of the real axis is obtained.

[1] Gokhberg I. Ts., Feldman I. A., Uravneniya v svertkakh i proektsionnye metody ikh resheniya, Nauka, M., 1971, 432 pp. | MR

[2] Pilidi V. S., “Obosnovanie metoda sglazhivaniya koeffitsientov dlya singulyarnykh integralnykh operatorov s kusochno-nepreryvnymi koeffitsientami”, Izv. vysshikh uchebnykh zavedenii. Sev.-Kavk. reg., 128:4 (2004), 9–12

[3] Pilidi V. S., “O metode sglazhivaniya koeffitsientov dlya singulyarnykh integralnykh operatorov”, Sovremennye metody i problemy teorii operatorov i garmonicheskogo analiza i ikh prilozheniya-IV, Tezisy dokladov, ZAO “Tsentr universalnoi poligrafii”, Rostov n/D, 2014, 38

[4] Pilidi V. S., “Kriterii ravnomernoi obratimosti regulyarnykh approksimatsii odnomernykh singulyarnykh integralnykh operatorov s kusochno-nepreryvnymi koeffitsientami”, Izv. AN SSSR. Ser. mat., 54:6 (1990), 1270–1294 | MR | Zbl

[5] Gokhberg I. Ts., Krupnik N. Ya., Vvedenie v teoriyu odnomernykh singulyarnykh integralnykh operatorov, “Shtiintsa”, Kishinev, 1973, 426 pp. | MR