Abstract
We study behavior of singular integral at neighborhood of the point at infinity. Its density satisfies the Hölder condition on the any finite part of the real axis, and at the infinity point it vanishes as power of logarithm with exponent lesser than −1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Muskhelishvili, N.I. Singular integral equations (Nauka, Moscow, 1968) [in Russian].
Gakhov, F.D. Boundary-value problems (Nauka, Moscow, 1977) [in Russian].
Salimov, R.B. “Behavior of the singular integral along the real axis with the density vanishing at infinity-near infinity”, Lobachevskii J. Math. 39(2), 266–270 (2018).
Fihtengolts, G.M. Course of differential and integral calculus, vol. 2 (Nauka, Moscow, 1970) [in Russian].
Salimov, R.B. “Behavior of singular integral with Hilbert kernel near point of weak continuity of its density”, Ufa matem. journ. 10(1), 83–95 (2018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 11, pp. 64–75.
About this article
Cite this article
Salimov, R.B. Behavior of Singular Integral Along the Real Axis with Density Vanishing Near Infinity Point. Russ Math. 63, 56–66 (2019). https://doi.org/10.3103/S1066369X19110082
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X19110082