%0 Journal Article
%T On the multi-dimensionel Favard Lemma
%A Abdallah Dhahri
%A Ameur Dhahri
%J Mathematics
%D 2013
%I arXiv
%X We prove that of the creator operators, on the $d$ commuting indeterminates polynomial algebra, are linearly independent. We further study the connection between the classical (one dimensional) and the multi-dimensional ($d$-dimensional, $d \geq 1$) Favard Lemmas. Moreover, we investigate the dependence of the Jacobi sequences on the linear change of basis of $\mathbb{C}^d$. Finally we prove that the Jacobi sequences associated to the probability measure product on $\mathbb{R}^d$ are diagonal matrices in the basis introduced by the tensor product of the orthogonal polynomials of the factor measures.
%U http://arxiv.org/abs/1310.8170v2