  This paper is devoted to study discrete and continuous bases for spaces
supporting representations of SO(3) and SO(3,2) where the spherical harmonics
are involved. We show how discrete and continuous bases coexist on appropriate
choices of rigged Hilbert spaces. We prove the continuity of relevant operators
and the operators in the algebras spanned by them using appropriate topologies
on our spaces. Finally, we discuss the properties of the functionals that form
the continuous basis.
