Abstract
Abstract We prove some properties of the Jacobi sequences and the creator operators, on the d commuting indeterminates polynomial algebra. Moreover, we prove that the matrix representations of the Jacobi sequences associated to product probability measures on ℝ d {\mathbb{R}^{d}} with finite moments of any order, are diagonal in the basis introduced by the tensor product of the orthogonal polynomials of the factor measures. Finally, we give a characterization of the atomic probability measures on ℝ d {\mathbb{R}^{d}} with finite number of atoms.
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