Two-Dimensional Diffusion Orthogonal Polynomials Ordered by a Weighted Degree.

We study the problem of describing the triples , , where is the (co)metric associated with a symmetric second-order differential operator defined on a domain of and such that there exists an orthonormal basis of consisting of polynomials which are eigenvectors of and this basis is compatible with the filtration of the space of polynomials by some weighted degree. In a joint paper of D. Bakry, M. Zani, and the author this problem was solved in dimension 2 for the usual degree. In the present paper we solve it still in dimension 2 but for a weighted degree with arbitrary positive weights. [ABSTRACT FROM AUTHOR]