A characterization of the \(L^2\)-range of the generalized spectral projections related to the Hodge-de Rham Laplacian

Let \(H^n(\mathbb R)\) be the real hyperbolic space. In this paper, we present a characterization of the \(L^2\)-range of the generalized spectral projections on the bundle of differential forms over \(H^n(\mathbb R)\). As an underlying result we show a characterization of the \(L^2\)-range of the Poisson transform on the bundle of differential forms on the boundary \(\partial H^n(\mathbb R)\). This gives a positive answer to a conjecture of Strichartz on differential forms.