Geodesic
Asymptotical representation of singular integral with the Hilbert kernel near a~point of weak continuity of density
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 58-62.

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We derive asymptotical representation of singular integral with the Hilbert kernel near a fixed point at which an integral density vanishes as a negative power of module of logarithm of a distance from variable point to a fixed one.
Keywords: asymptotical representation, singular integral, Hölder condition, weak continuity.
Mots-clés : Hilbert kernel 
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R. B. Salimov. Asymptotical representation of singular integral with the Hilbert kernel near a~point of weak continuity of density. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2015), pp. 58-62. http://geodesic.mathdoc.fr/item/IVM_2015_7_a5/

[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] Salimov R. B., Shmagin Yu. A., “Ob issledovanii povedeniya singulyarnogo integrala s yadrom Gilberta vblizi tochki slaboi nepreryvnosti plotnosti”, Tr. matem. tsentra im. N. I. Lobachevskogo, 46, 2013, 399–402

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