Orthogonal polynomials and diffusion operators
Probability
2021-05-28 v3
Abstract
We want to describe the triplets (\Omega, (g), \mu) where (g) is the (co)metric associated to some symmetric second order differential operator L defined on the domain \Omega of R^d and such that L is expandable on a basis of orthogonal polynomials of L_2(\mu), and \mu is some admissible measure. Up to affine transformation, we find 11 compact domains in dimension 2, and also give some non--compact cases in this dimension.
Cite
@article{arxiv.1309.5632,
title = {Orthogonal polynomials and diffusion operators},
author = {Dominique Bakry and Stepan Orevkov and Marguerite Zani},
journal= {arXiv preprint arXiv:1309.5632},
year = {2021}
}