On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals

For a class of integral equations of the first kind whose kernels are discontinuous on the diagonals, the convergence of the Lavrent??ev regularization method is proved by using methods of the spectral theory of integral operators. These methods lead to a special Dirac system, and finding the asymptotics of fundamental solutions is an important part of the proof.