  The Fredholm integral equations of the first kind is a typical ill-posed
problem, so that it is usually difficult to obtain its analytical minimal-norm
solution. This paper gives a closed-form minimal-norm solution for the
degenerate kernel equations based on the H-HK formulation. Furthermore, it has
been shown that the structure of solutions to degenerate kernel equations and
matrix equations are consistent. Subsequently, the obtained results are
extended to non-degenerate integral equations. Finally, the validity and
applicability of the proposed method are demonstrated by some examples.
