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Статья
2015

Asymptotical representation of singular integral with the Hilbert kernel near a point of weak continuity of density


R. B. SalimovR. B. Salimov
Русская математика
https://doi.org/10.3103/S1066369X15070063
Abstract / Full Text

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.

Author information
  • Kazan State Architecture and Building University, ul. Zelyonaya 1, Kazan, 420043, RussiaR. B. Salimov
References
  1. 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).
  2. 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).
  3. Muskhelishvili, N. I. Singular Integral Equations (Nauka, Moscow, 1968).