A constructive method for the solution of integral equations with Hilbert kernel

We propose and prove a constructive method for the solution of linear singular integral equations with Hilbert kernel. In this method, in contrast to the methods applied earlier, the singular operator is approximated by operators that preserve the main properties of this operator, which makes it possible to obtain estimates that are more exact from the point of view of convergence rate. In addition, this method requires less computations because it allows one to find approximate solutions explicitly (not only at isolated points) and the coefficients of the corresponding systems of algebraic equations are easily calculated.