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We consider the Schr\"odinger operator with a potential q on a disk and themap that associates to q the corresponding Dirichlet to Neumann (DtN) map. Wegive some numerical and analytical results on the range of this map and itsstability, for the particular class of one-step radial potentials.

The Dirichlet-to-Neumann map in a disk with a one-step radial potential. An analytical and numerical study