A mechanism for localization of quantum fields on a s-brane, representing the boundary of a s+2 dimensional bulk space, is investigated. Minkowski and AdS bulk spaces are analyzed. Besides the background geometry, the relevant parameters controlling the theory are the mass M and a real parameter η, specifying the boundary condition on the brane. The importance of exploring the whole range of allowed values for these parameters is emphasized. Stability in Minkowski space requires η to be greater

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... or equal to -M, whereas in the AdS background all real η are permitted. Both in the flat and in AdS case, the induced field on the brane is a non-canonical generalized free field. For a suitable choice of boundary condition, corresponding to the presence of a boundary state, the induced field on the brane mimics standard s+1 dimensional physics. In a certain range of η, the spectral function in the the AdS case is ominated by a massive excitation, which imitates the presence of massive particle on the brane. We show that the quantum field induced on the brane is stable.