International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B, ch. 1.3, p. 69

The general statement of Parseval's theorem given in Section 1.3.4.2.1.5 may be rewritten in terms of symmetryunique structure factors and electron densities by means of orbit decomposition.
In reciprocal space, for each l, the summands corresponding to the various are equal, so that the lefthand side is equal to
In real space, the triple integral may be rewritten as (where D is the asymmetric unit) if and are smooth densities, since the set of special positions has measure zero. If, however, the integral is approximated as a sum over a Ginvariant grid defined by decimation matrix N, special positions on this grid must be taken into account: where the discrete asymmetric unit D contains exactly one point in each orbit of G in .