论文标题
二维扩散正交多项式按加权程度排序
Two-dimensional diffusion orthogonal polynomials ordered by a weighted degree
论文作者
论文摘要
我们研究以下问题：描述三胞胎$（ω，g，μ）$，$μ=ρ\，dx $，其中$ g =（g^{ij}（x））$是与对称的二阶差异操作员相关的（CO）度量， $ \ mathbb r^d $在域上定义的ρ\ partial_j f）$，因此存在由$ \ mathcal l^2（μ）$的正顺序基础，该$由$ l $的多项式制成，在某些体重程度上排名polynomials。 在与D. bakry和M. Zani的联合论文中，该问题在通常的程度上在维度2中解决了。在本文中，我们将其求解仍处于维度2，但以任意正权重的加权程度。
We study the following problem: describe the triplets $(Ω,g,μ)$, $μ=ρ\,dx$, where $g= (g^{ij}(x))$ is the (co)metric associated with the symmetric second order differential operator $L (f) = \frac{1}ρ\sum_{ij} \partial_i (g^{ij} ρ\partial_j f)$ defined on a domain $Ω$ of $\mathbb R^d$ and such that there exists an orthonormal basis of $\mathcal L^2(μ)$ made of polynomials which are eigenvectors of $L$, where the polynomials are ranked according to some weighted degree. In a joint paper with D. Bakry and M. Zani 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.
