Characteristic value of a kernel

Summary

A characteristic value of a kernel $K$ is a number $\lambda$ for which the homogeneous integral equation $\varphi(x) = \lambda \int K(x, y) \varphi(y) \, dy$ has a nonzero solution. It is the reciprocal of a nonzero eigenvalue of the integral operator with kernel $K$. Characteristic values are the exceptional parameters of the Fredholm equation of the second kind. Away from them, the equation has exactly one solution for each right-hand side.