Justifying the convergence of the rectangular method for complete singular integral equations with continuous coefficients on the circle (Q2387836)

A method of solution for a complete singular integral equation \((aI+bS+K)f=g\) on the unit circle \(\Gamma\) is obtained based on the discretization of integral operators by the rectangle rule, where \(a\) and \(b\) are Hölder functions satisfying the strong ellipticity condition, \(S\) is an integral operator with Hölder kernel and \(I\) is the unit operator. This method is justified under the assumption that the equation is solvable in \(L_2(\Gamma)\).