Diffusions with polynomial eigenvectors via finite subgroups of O(3)

TL;DR

This paper introduces new diffusion operators in two and three dimensions with orthogonal polynomial eigenvectors, constructed using finite subgroups of O(3) and their invariant polynomials, expanding the class of such operators.

Contribution

It presents novel examples of diffusion operators with polynomial eigenvectors based on finite subgroups of O(3), a new approach in the field.

Findings

New diffusion operators with polynomial eigenvectors in 2D and 3D

Construction method using finite subgroups of O(3)

Identification of invariant polynomials for these groups

Abstract

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