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.
