Solution to the Volterra Operator Equations of the 1st kind with Piecewise Continuous Kernels

The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of solutions are constructed in case of non-unique solution. The algorithm for the solution's improvement is proposed using the successive approximations method.
Comment: 17 pages