We develop and describe continuous and discrete transforms of class functionsView original: http://arxiv.org/abs/1202.0476
on a compact semisimple, but not simple, Lie group $G$ as their expansions into
series of special functions that are invariant under the action of the even
subgroup of the Weyl group of $G$. We distinguish two cases of even Weyl groups
-- one is the direct product of even Weyl groups of simple components of $G$,
the second is the full even Weyl group of $G$. The problem is rather simple in
two dimensions. It is much richer in dimensions greater than two -- we describe
in detail $E-$transforms of semisimple Lie groups of rank 3.