  We present a formalism describing the physical content of cross-correlation
functions between a diffuse background and a population of discrete sources.
The formalism is used to interpret cross-correlation signals between the
unresolved X-ray background and a galaxy population resolved to high redshift
in another spectral band. Specifically, we apply it to the so-called faint blue
galaxy population and constrain their X-ray emissivity and clustering
properties. A model is presented which satisfies the recently measured
constraints on all 3 correlation functions (galaxy/galaxy,
background/background and galaxy/background). This model predicts that faint
galaxies in the magnitude range B=18-23 (cvering redshifts $z \lsim 0.5$) make
up $\sim 22 \%$ of the X-ray background in the 0.5-2 keV band. At the mean
redshift of the galaxy sample, $\bar z=0.26$, the comoving volume emissivity is
$\rho_X \sim 6-9 \times 10^{38}h$ ergs s$^{-1}$Mpc$^{-3}$ . When extrapolated
to fainter magnitudes, the faint blue galaxy population can account for most of
the residual background at soft energy. We show how the measurement of the
angular and zero-lag cross-correlation functions between increasingly faint
galaxies and the X-ray background can allow us to map the X-ray emissivity as a
function of redshift.
