  Precise asymptotics known for the Green's function of the Laplace operator
have found their analogs for periodic elliptic operators of the second order at
and below the bottom of the spectrum. Due to the band-gap structure of the
spectra of such operators, the question arises whether similar results can be
obtained near or at the edges of spectral gaps. As the result of this work
shows, this is possible at a spectral edge in dimensions d>2.
