Integrals of products of eigenfunctions on SL 2 ( C )

In a variety of situations, integrals of products of eigenfunctions have faster decay than smoothness entails. This phenomenon does not appear for abelian or compact groups, since irreducibles are finite-dimensional, so the decomposition of a tensor product of irreducibles is finite. In contrast, for non-compact, nonabelian groups irreducibles are typically infinite-dimensional, and the decomposition of a tensor product of irreducibles typically contains infinitely-many irreducibles, and the issue is non-trivial.