  In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an
asymptotic form of Schur's orthogonality for tempered irreducible unitary
representations of semisimple groups defined over local fields. In the
non-Archimedean case, they established such an orthogonality for $K$-finite
matrix coefficients. Building on their work, and exploiting the admissibility
of irreducible unitary representations, we prove the analogous result in the
Archimedean case.
