Good morning. How can we prove that
$$ \Gamma (s,t, \Lambda ) - \Gamma (s,t, M ) = \Lambda - M \times \int { \Gamma(s,t, \Lambda ) \times \Gamma (s,t,M) \, dx }$$
I tried to use the formula of resolvent kernel $$ \Gamma (s, t,\Lambda) = \sum_{m=1}^\infty \Lambda ^{m-1} \times k_m ( s, t, \Lambda ) $$ Where $$ k (s,t ,\Lambda ) $$ is the kernel function with the variables s and t and the eigenvalues are $$ \Lambda and M $$