Orthogonal polynomials and diffusions operators

Dominique Bakry (1, 2) , Stepan Orevkov (1) , Marguerite Zani (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IUF - Institut universitaire de France
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: orthogonal polynomials; Lie groups

Domaines: Probabilités [math.PR]

Dominique Bakry, Stepan Orevkov, Marguerite Zani. Orthogonal polynomials and diffusions operators. 2013. ⟨hal-00864331⟩