Orthogonal polynomials and diffusions operators

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.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00864331
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Submitted on : Sunday, September 22, 2013 - 7:40:14 PM
Last modification on : Friday, October 11, 2019 - 8:22:41 PM
Long-term archiving on : Friday, April 7, 2017 - 12:51:28 AM

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  • HAL Id : hal-00864331, version 1
  • ARXIV : 1309.5632

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

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