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Spectra of self-gradients on spheres. (English) Zbl 1012.22026
In the paper under review the author gives a general formula for the spectral resolution of a class of first-order differential operators on the sphere $$S^n$$ which includes, among the most elementary cases, the Dirac and the Rarita-Schwinger operators.

##### MSC:
 22E46 Semisimple Lie groups and their representations 43A85 Harmonic analysis on homogeneous spaces 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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