feature map and eigenfunctions of a kernel ?

Hi,

I know that a for a Mercer kernel I have :

$k(x,y) = \int_{-\infty}^{\infty} [\Phi(x)]_\lambda^* [\Phi(y)]_\lambda d\lambda = < [\Phi(x)]_\lambda, [\Phi(y)]_\lambda>$

how is $[\Phi(x)]_\lambda$ related to the eigenfunctions of the kernel ?

I'm not very familiar with these concepts so please be patient

Alexis