Geodesic
Justifying the convergence of the rectangular method for complete singular integral equations with continuous coefficients on the circle
Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 163-175 
M. É. Abramyan. Justifying the convergence of the rectangular method for complete singular integral equations with continuous coefficients on the circle. Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 163-175. http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a0/
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     title = {Justifying the convergence of the rectangular method for complete singular integral equations with continuous coefficients on the circle},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For an integral equation on the unit circle $\Gamma$ of the form $(aI+bS+K)f=g$, where $a$ and $b$ are Hölder functions, $S$ is a singular integration operator, and $K$ is an integral operator with Hölder kernel, we consider a method of solution based on the discretization of integral operators using the rectangle rule. This method is justified under the assumption that the equation is solvable in $L_2(\Gamma)$ and the coefficients $a$ and $b$ satisfy the strong ellipticity condition.

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