Abstract
We obtain an asymptotic representation of singular integral with the Hilbert kernel near a point, where modulus of continuity of its density behaves itself as inverse value of double 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”, RussianMathematics (Iz. VUZ) 57, No. 6, 32–38 (2013).
Muskhelishvili, N. I. Singular Integral Equations (Nauka, Moscow, 1968) [in Russian].
Gradshtein, I. S., Ryzhik, I.M. Tables of Integrals, Sums, Series and Products (Fizmatgiz, Moscow, 1963) [in Russian].
Fikhtengol’tz, G. M. Course of Differential and Integral Calculus (Nauka, Moscow, 1970), Vol. II [in Russian].
Evgrafov, M. A. Asymptotic Estimates and Entire Functions (Nauka, Moscow, 1979) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © R.B. Salimov, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 4, pp. 93–96.
About this article
Cite this article
Salimov, R.B. New asymptotic representation for singular integral with Hilbert kernel near a point of weak continuity of density. Russ Math. 60, 60–64 (2016). https://doi.org/10.3103/S1066369X16040095
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X16040095