  We consider a homogenization of elliptic spectral problem stated in a
perforated domain, Fourier boundary conditions being imposed on the boundary of
perforation. The presence of a locally periodic coefficient in the boundary
operator gives rise to the effect of a localization of the eigenfunctions.
Moreover, the limit behaviour of the lower part of the spectrum can be
described in terms of an auxiliary harmonic oscillator operator. We describe
the asymptotics of the eigenpairs and derive the estimates for the rate of
convergence.
