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

On Kazhdan-Yom Din asymptotic Schur orthogonality for K-finite matrix coefficients