  Let H=O(n)xO(1) be an anisotropic subgroup of G=O(n, 1) and let A be the
adele ring of k=Q. Consider the periods of an Eisenstein series on G against a
form F on H. Relying on a variant of Levi-Sobolev spaces, we describe certain
Poincar\'e series as fundamental solutions for the laplacian, and use them to
establish a spectral identity concerning the second moments (in F-aspect) of
the Eisenstein series.
