  The paper discusses relations between the structure of the complex Fermi
surface below the spectrum of a second order periodic elliptic equation and
integral representations of certain classes of its solutions. These integral
representations are analogs of those previously obtained by S. Agmon, S.
Helgason, and other authors for solutions of the Helmholtz equation (i.e., for
generalized eigenfunctions of Laplace operator). In a previous joint work with
Y. Pinchover we described all solutions that can be represented as integrals of
positive Bloch solutions over the imaginary Fermi surface, with a hyperfunction
as a ``measure''. Here we characterize the class of solutions such that the
corresponding hyperfunction is a distribution on the Fermi surface.
