Geodesic
New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 73-78.

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 module of 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_2016_4_a8,
     author = {R. B. Salimov},
     title = {New asymptotic representation 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 = {73--78},
     publisher = {mathdoc},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/}
}
TY  - JOUR
AU  - R. B. Salimov
TI  - New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 73
EP  - 78
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/
LA  - ru
ID  - IVM_2016_4_a8
ER  - 
%0 Journal Article
%A R. B. Salimov
%T New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 73-78
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/
%G ru
%F IVM_2016_4_a8
R. B. Salimov. New asymptotic representation of a~singular integral with the Hilbert kernel near a~point of weak continuity of its density. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 73-78. http://geodesic.mathdoc.fr/item/IVM_2016_4_a8/

[1] Salimov R. B., “K povedeniyu singulyarnogo integrala s yadrom Gilberta vblizi tochki slaboi nepreryvnosti plotnosti”, Izv. vuzov. Matem., 2013, no. 6, 37–44 | MR | Zbl

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

[3] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatgiz, M., 1963 | MR

[4] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. II, Nauka, M., 1970

[5] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR