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Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 266–270 | Cite as

Behavior of the Singular Integral Along the Real Axis with the Density Vanishing at Infinity Near Infinity

  • R. B. Salimov
Article
  • 9 Downloads

Abstract

We study the behavior of singular integral along the real axis in the neighborhood of the point at infinity, when its density satisfy Hölder condition in any finite part of the real axis and is continuous function in the neighborhood of the point at infinity, which decreases with the order of decreasing same as the lower then the minus first power of logarithm of the absolute value of the coordinate of the point of the real axis, when we move this point unlimitedly from the origin.

Keywords and phrases

singular integral Hölder condition Reimann boundary value problem Hilbert boundary value problem 

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References

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    N. I. Muskhelishvili, Singular Integral Equations (Nauka, Moscow, 1968) [in Russian].zbMATHGoogle Scholar
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    F. D. Gakhov, Boundary-Value Problems (Nauka, Moscow, 1977) [in Russian].zbMATHGoogle Scholar
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    F.M. Fikhtengolz, Course ofDifferential and Integral Calculus (Nauka, Moscow, 1970), Vol. 2 [inRussian].Google Scholar
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    R. B. Salimov, “Asymptotical representation of singular integral with the Hilbert kernel near a point of weak continuity of density,” Russ. Math. 59 (7), 52–55 (2015).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan State University of Architecture and EngineeringKazan, TatarstanRussia

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