Abstract
This article presents a method for the determination of the eigenvalues and eigenfunctions of Fredholm's linear integral equation with a positive definite root, which is the correlation function of a function of a random variable, and is related to the phenomenon of white noise by a linear differential equation. This method is a modification of the method given in article [1] for the solution of an integral equation of the first kind, occuring in the statistical theory of optimal systems.
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