Perturbation of eigenvalues

Question

I am looking at a certain operator, that is a Hilbert-Schmidt integral operator from $L^2(X,d\mu)$ to $L^2(X,d\mu)$. The question is how eigenvalues, or singular values, change as it's kernel is perturbed. Particularly let's throw in $\epsilon>0$ and consider the eigenvalues of operator induced by $K'(x,y):=K(\epsilon x,y)$ where $K(x,y)$ is the original kernel. Any reference, to a right source, is highly appreciated.