In this paper, we study a new type of inverse problem on warped product
    Riemannian manifolds with connected boundary that we name warped balls. Using
    the symmetry of the geometry, we first define the set of Regge poles as the
    poles of the meromorphic continuation of the Dirichlet-to-Neumann map with
    respect to the complex angular momentum appearing in the separation of
    variables procedure. These Regge poles can also be viewed as the set of
    eigenvalues and resonances of a one-dimensional Schr\”odinger equation on the
    half-line, obtained after separation of variables. Secondly, we find a precise
    asymptotic localisation of the Regge poles in the complex plane and prove that
    they uniquely determine the warping function of the warped balls.

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