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We consider inverse obstacle and transmission scattering problems where thesource of the incident waves is located on a smooth closed surface that is aboundary of a domain located outside of the obstacle/inhomogeneity of themedia. The domain can be arbitrarily small but fixed.The scattered waves aremeasured on the same surface. An effective procedure is suggested for recoveryof interior eigenvalues by these data.

Recovery of interior eigenvalues from reduced near field data