# Eigenvalues of an integral operators

Dear all, I want to find the first eigenvalues (and even the eigenvectors if possible) of a difference operator

$$G(y) = \int_0^1 V( t - y ) F(t) dt$$

The function $V$ is given by some infinite series and is easily computable to any decent degree of accuracy. This is a very classical problem, but I wouldn't want to rediscover the wheel if there is a shop that sells some :) Many thanks in advance, Olivier

Do you mean $G(F)(y)$? Or what is $F$?

Yes, G(F)(y). A basic answer consists in approximating the integral. Wiith Simpson's formula, this gives

where Wstar(y) is my kernel function (which is even and vanishes at 0). This gives an idea, but the above has no control of approximation. I would like to find something more refined. Best, Olivier