Geodesic
Behavior of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 37-44.

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

We study the behavior of a singular integral with the Hilbert kernel near a fixed point, where the density vanishes as the value inverse to the logarithm of the distance from this point to a variable one, and the integral is not necessarily convergent.
Keywords: singular integral, Hölder condition, weak continuity.
Mots-clés : Hilbert kernel 
@article{IVM_2013_6_a3,
     author = {R. B. Salimov},
     title = {Behavior of a~singular integral with the {Hilbert} kernel near a~point of weak continuity of its density},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--44},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_6_a3/}
}
TY  - JOUR
AU  - R. B. Salimov
TI  - Behavior of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 37
EP  - 44
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_6_a3/
LA  - ru
ID  - IVM_2013_6_a3
ER  - 
%0 Journal Article
%A R. B. Salimov
%T Behavior of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 37-44
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_6_a3/
%G ru
%F IVM_2013_6_a3
R. B. Salimov. Behavior of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 37-44. http://geodesic.mathdoc.fr/item/IVM_2013_6_a3/

[1] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR | Zbl

[2] Salimov R. B., “K vychisleniyu singulyarnykh integralov s yadrom Gilberta”, Izv. vuzov. Matem., 1970, no. 12, 93–96 | MR | Zbl

[3] Bari N. K., Stechkin S. B., “Nailuchshie priblizheniya i differentsialnye svoistva dvukh sopryazhennykh funktsii”, Tr. Moskovsk. matem. o-va, 5, 1956, 483–522 | MR | Zbl

[4] Krikunov Yu. M., “O zadache Trikomi s proizvodnymi v kraevom uslovii”, Uchen. zap. Kazansk. un-ta, 122, no. 3, 1962, 30–53 | MR | Zbl

[5] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 3, Nauka, M., 1970

[6] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Nauka, M., 1970

[7] Mityushev V., “Hilbert boundary value problem for multiply connected domains”, Complex Variables, 35:4 (1998), 283–295 | DOI | MR | Zbl

[8] Bezrodnykh S. I., Vlasov V. I., “Zadacha Rimana–Gilberta v slozhnoi oblasti dlya modeli magnitnogo peresoedineniya v plazme”, Zhurn. vychisl. matem. i matem. fiz., 42:3 (2002), 277–312 | MR | Zbl

[9] Salimov R. B., Shabalin P. L., “Zadacha Gilberta so schetnym mnozhestvom tochek razryva pervogo roda u koeffitsientov i konechnym indeksom”, Izv. vuzov. Matem., 2010, no. 3, 36–47 | MR | Zbl

[10] Salimov R. B., “Vidoizmenenie novogo podkhoda k resheniyu kraevoi zadachi Gilberta dlya analiticheskoi funktsii v mnogosvyaznoi oblasti”, Izv. vuzov. Matem., 2011, no. 11, 46–57 | MR | Zbl

[11] Salimov R. B., “O povedenii singulyarnogo integrala s yadrom Gilberta vblizi tochki slaboi nepreryvnosti plotnosti”, Izv. vuzov. Matem., 2012, no. 6, 61–66 | Zbl