Abstract
We derive an asymptotical representation for singular integral with the Hilbert kernel near a fixed point where its density vanishes as a negative power of module of logarithm of distance from this point.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Salimov, R. B. “Behavior of a Singular Integral with Hilbert Kernel at a Point of Weak Continuity of Its Density,” Russian Mathematics (Iz. VUZ) 57, No. 6, 32–38 (2013).
Salimov, R. B. and Shmagin, Yu. A. “Investigation of Behavior of a Singular Integral with Hilbert Kernel at a Point ofWeak Continuity of its Density,” Trudy LobachevskiiMat. Tsentra 46, 399–402 (2013).
Muskhelishvili, N. I. Singular Integral Equations (Nauka, Moscow, 1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R.B. Salimov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 7, pp. 58–62.
About this article
Cite this article
Salimov, R.B. Asymptotical representation of singular integral with the Hilbert kernel near a point of weak continuity of density. Russ Math. 59, 52–55 (2015). https://doi.org/10.3103/S1066369X15070063
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X15070063