Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution (Q674429)

The paper provides a convergence analysis with respect to weighted uniform norms of polynomial approximation methods for solving Cauchy singular integral equations with compact perturbations on an interval. Weighted spaces of continuous functions are defined depending on the order of best weighted uniform approximation by polynomials. The authors study the mapping properties of the Cauchy singular operator as well as of integral operators with regular and weakly singular kernels within these spaces. They prove stability and convergence of special collocation and quadrature methods for perturbed singular integral equations and report on some numerical examples.