Symmetric diffusions with polynomial eigenvectors

Dominique Bakry

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arXiv · 1403.7468

Symmetric diffusions with polynomial eigenvectors

Dominique Bakry

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Abstract

We describe symmetric diffusion operators where the spectral decomposition is given through a family of orthogonal polynomials. In dimension one, this reduces to the case of Hermite, Laguerre and Jacobi polynomials. In higher dimension, some basic examples arise from compact Lie groups. We give a complete description of the bounded sets on which such operators may live. We then provide a classification of those sets when the polynomials are ordered according to their usual degrees

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Dominique Bakry. 2014-03-28. Symmetric diffusions with polynomial eigenvectors. https://arxiv.org/abs/1403.7468

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