Orthogonal polynomials and diffusion operators

Dominique Bakry; Stepan Orevkov; Marguerite Zani

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arXiv · 1309.5632

Orthogonal polynomials and diffusion operators

Dominique Bakry·Stepan Orevkov·Marguerite Zani

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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 L_2(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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BibTeX RIS

Dominique Bakry, Stepan Orevkov, Marguerite Zani. 2021-05-27. Orthogonal polynomials and diffusion operators. https://arxiv.org/abs/1309.5632

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