  By applying projection operators to state vectors of coordinates we obtain
subspaces in which these states are no longer normalized according to Dirac's
delta function but normalized according to what we call "incomplete delta
functions". We show that this class of functions satisfy identities similar to
those satisfied by the Dirac delta function. The incomplete delta functions may
be employed advantageously in projected subspaces and in the link between
functions defined on the whole space and the projected subspace. We apply a
similar procedure to finite dimensional vector spaces for which we define
incomplete Kronecker deltas. Dispersion relations for the momenta are obtained
and ''sums over poles'' are defined and obtained with the aid of differences of
incomplete delta functions.
