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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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