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First, we consider the class $\\mathcal{A}$ of potentials $q(r)$ which can be extended analytically in $\\Re z \\geq 0$ such that $\\mid q(z)\\mid \\leq C \\ (1+ \\mid z \\mid )^{-\\rho}$, $\\rho \\textgreater{} \\frac{3}{2}$. If $q$ and $\\tilde{q}$ are two such potentials  and if the corresponding phase shifts $\\delta\\_l$ and $\\tilde{\\delta}\\_l$  are super-exponentially close, then $q=\\tilde{q}$. 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