Reconstruction of the convolution operator from the right-hand side on the real half-axis

We study a Volterra integral equation of the first kind in convolutions on a semi-infinite interval. Under rather natural constraints on the kernel and the right-hand side of a Volterra integral equation (the kernel has bounded support and the support of the right-hand side may be unbounded), it is possible to reconstruct the integral operator of the equation (the solution and the kernel of the integral operator) from the right-hand side of the equation. Some uniqueness theorem is proved, as well as necessary and sufficient conditions for solvability and the explicit formulas for the solution and the kernel are obtained.