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Let $G=\operatorname{O}(1,n+1)$ with maximal compact subgroup $K$ and let$\Pi$ be a unitary irreducible representation of $G$ with non-trivial$(\mathfrak{g},K)$-cohomology. Then $\Pi$ occurs inside a principal seriesrepresentation of $G$, induced from the $\operatorname{O}(n)$-representation$\bigwedge\nolimits^p(\mathbb{C}^n)$ and characters of a minimal parabolicsubgroup of $G$ at the limit of the complementary series. Considering thesubgroup $G'=\operatorname{O}(1,n)$ of $G$ with maximal compact subgroup $K'$,we prove branching laws and explicit Plancherel formulas for the restrictionsto $G'$ of all unitary representations occurring in such principal series,including the complementary series, all unitary $G$-representations withnon-trivial $(\mathfrak{g},K)$-cohomology and further relative discrete seriesrepresentations in the cases $p=0,n$. Discrete spectra are constructedexplicitly as residues of $G'$-intertwining operators which resemble theFourier transforms on vector bundles over the Riemannian symmetric space$G'/K'$.

Branching of unitary $\operatorname{O}(1,n+1)$-representations with non-trivial $(\mathfrak{g},K)$-cohomology