Fredholm integral equation

In mathematics, the Fredholm integral equation introduced by Ivar Fredholm gives rises to a Fredholm operator. From the point of view of functional analysis it therefore has a well-understood abstract eigenvalue theory. In this case that is supported by a computational theory, including the Fredholm determinants.

Writing K for the integration operator determined by the continuous kernel function K(x,y) on an interval [a,b] of the real line, a Fredholm integral operator is of type I + K, and the typical integral equation to solve is of the inhomogeneous type (I + K)f = g where g is a given function on [a,b].