Fredholm minors

Summary

The Fredholm minors of a continuous kernel $K$ are entire functions of the parameter $\lambda$. They are built like the Fredholm determinant, from determinants of values of $K$, but with some rows and columns held at fixed points. They are the integral analogues of the minors and cofactors of the matrix $I - \lambda A$. The first minor divided by the Fredholm determinant is the resolvent kernel. So the minors give the explicit solution of the Fredholm equation of the second kind. At a zero of the determinant, the first minor that is not identically zero yields the solutions of the homogeneous equation.