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Diffusions with polynomial eigenvectors via finite subgroups of \(O(3)\). (English. French summary) Zbl 1369.35038

Summary: We provide new examples of diffusion operators in dimension 2 and 3 which have orthogonal polynomials as eigenvectors. Their construction relies on the finite subgroups of \(O(3)\) and their invariant polynomials.

MSC:

35P10 Completeness of eigenfunctions and eigenfunction expansions in context of PDEs
60D05 Geometric probability and stochastic geometry
58J65 Diffusion processes and stochastic analysis on manifolds
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