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We consider the Hankel multidimensional operatorΔα\Delta_{\alpha},α=(α1,…,αn)∈]−12,+∞[n\alpha=(\alpha_{1},\dots,\alpha_{n})\in\mathopen{]}-\frac{1}{2},+\infty\mathclose{[}^{n}, defined on]0,+∞[n\mathopen{]}0,+\infty\mathclose{[}^{n}by

The Wigner transformation associated with the Hankel multidimensional operator