Abstract
In paper [1] the d-dimensional analogue of the Jacobi parameters has been individuated in a pair of sequences ((a.|n0),(Ω∼n)), where (a.|n0) is a sequence of Hermitean matrices and Ω∼n(n ∈ ℕ) a positive definite kernel with values in the linear operators on the n-th space of the orthogonal gradation. In this paper we prove that product measures on ℝd are characterized by the property that the (a.|n0) are diagonal and the (Ω∼n) quasidiagonal (see Definition 2 below) in the orthogonal polynomial basis.
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