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Laplacians on spheres. (English) Zbl 1405.43007
Authors’ abstract: Spheres can be written as homogeneous spaces \(G/H\) for compact Lie groups in a small number of ways. In each case, the decomposition of \(L^2(G/H)\) into irreducible representations of \(G\) contains interesting information. We recall these decompositions, and see what they can reveal about the analogous problem for noncompact real forms of \(G\) and \(H\).

MSC:
43A85 Harmonic analysis on homogeneous spaces
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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