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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, weak continuity.
Mots-clés : Hilbert kernel, Hölder condition 
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     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},
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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