Application of the abstract theory of operators in the approximate solution of boundary problems and singular integral equations. (Q2755985)

Let \(L\) be a closed rectifiable Jordan curve in the complex plane, \(S_L\) be the space of functions defined on \(L\) which can be represented as a sum of boundary values of functions analytic inside and outside of \(L\) and continuous up to \(L\). One-dimensional singular integral operators acting in \(S_L\) and having coefficients which satisfy the Dini condition are considered. The author obtains norm estimates for such operators and their inverses and for differences of solutions of corresponding singular integral equations and of perturbed ones.