Geodesic
A method of construction of the solution of singular integral equation with Cauchy kernel
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2007), pp. 3-16

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Basing on the methods of the theory of boundary-value problems for analytic functions, the paper constructs generalized eigenfunctions of integral operator generating by Cauchy kernel in a finite interval. Further formulas for generalized integral Fourier transform by these eigenfunctions are obtained. Then the results are applied to construct solutions of singular integral equations with Cauchy kernel and constant coefficients. 
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A. B. Grigoryan. A method of construction of the solution of singular integral equation with Cauchy kernel. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2007), pp. 3-16. http://geodesic.mathdoc.fr/item/UZERU_2007_1_a0/