Fredholm theory

Summary

Fredholm theory is the theory of the Fredholm equation of the second kind $\varphi - \lambda T_K \varphi = f$. In its classical form it builds the solution from the Fredholm determinant and the Fredholm minors, entire functions of $\lambda$. It proves Fredholm's theorem: the equation behaves like a square linear system. Its abstract form is the spectral theory of compact operators on Banach spaces, and it leads to the notion of a Fredholm operator. It was one of the sources of functional analysis.