  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 \eta,
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 \eta to be greater or equal to -M, whereas in the AdS
background all real \eta 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 \eta, 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.
