Orthogonal polynomials and diffusion operators

2013/09/22 by Bakry, Dominique, Orevkov, Stepan, Zani, Marguerite · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1309.5632

Abstract

We want to describe the triplets (Ω, (g), μ) where (g) is the (co)metric associated to some symmetric second order differential operator L defined on the domain Ωof R^d and such that L is expandable on a basis of orthogonal polynomials of L₂(μ), and μis 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.

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