  Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell
bundles over the Pontrjagin dual of G as continuous spectral decompositions of
G-actions on C*-algebras. We classify such spectral decompositions using
certain dense subspaces related to Marc Rieffel's theory of
square-integrability. There is a unique continuous spectral decomposition if
the group acts properly on the primitive ideal space of the C*-algebra. But
there are also examples of group actions without or with several inequivalent
spectral decompositions.
