Scattering and a Plancherel formula of spherical varieties for real reductive split groups

Abstract: We establish the analog for real spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh (\cite{SV}, Theorem 7.3.1) for p-adic spherical varieties. We use properties of the Harish-Chandra homomorphism of Knop for invariant differential operators of the variety, special coverings of the variety and spectral projections.