A new construction of Juhl's conformally covariant differential operators from $S^n$ to $S^{n-1}$ (or from $\mathbb R^n$ to $\mathbb R^{n-1}$) is proposed. They are obtained as the composition of a new family of differential operators on $S^n$, covariant under the subgroup of conformal transformations of $S^n$ preserving $S^{n-1}$, followed by the restriction from $S^n$ to $S^{n-1}$.
Center of U(n), Cascade of Orthogonal Roots, and a Construction of Lipsman-Wolf
Construction of Tame Types
Construction and analysis of symmetry breaking operators for the pair $(\operatorname{GL}(n+1,\mathbb{R}),\operatorname{GL}(n,\mathbb{R}))$
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