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Another approach to Juhl’s conformally covariant differential operators from $$S^n$$ to $$S^{n-1}$$. (English) Zbl 1365.58020
Summary: A family $$({\mathbf D}_\lambda)_{\lambda\in \mathbb C}$$ of differential operators on the sphere $$S^n$$ is constructed. The operators are conformally covariant for the action of the subgroup of conformal transformations of $$S^n$$ which preserve the smaller sphere $$S^{n-1}\subset S^n$$. The family of conformally covariant differential operators from $$S^n$$ to $$S^{n-1}$$ introduced by A. Juhl is obtained by composing these operators on $$S^n$$ and taking restrictions to $$S^{n-1}$$.

MSC:
 58J70 Invariance and symmetry properties for PDEs on manifolds 43A85 Harmonic analysis on homogeneous spaces
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References:
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