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 Rd 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 Rd with finite number of atoms.

On the multi-dimensional Favard lemma

Dhahri A.;
2017-01-01

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 Rd 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 Rd with finite number of atoms.
2017
Atomic probability measure
Multi-dimensional favard lemma
Product probability measure
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1152039
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