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.


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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