S Helgason 
Analysis on Lie Groups and Homogeneous Spaces [PDF ebook] 

The theme of this volume is a treatment of differential equations on a $C^/infty$ manifold $V$ by separation of variables techniques. More specifically, given a Lie transformation group $L$ of $V$ and a Lie subgroup $H/subset L$, if $D(V)$ is the set of differential operators on $V$ invariant under $L$, then the principal object of study is the set of distributions $T$ on $V$ satisfying the following two conditions:(i) $T$ is an eigendistribution of each $D/in D(V)$; (ii) $T$ is invariant under $H$.