  We present the galaxy rest-frame near-IR Luminosity Function (LF) and its
cosmic evolution to z=1.5 based on a spectroscopic survey of a magnitude
limited sample of galaxies with Ks<20 (the K20 survey, Cimatti et al. 2002b).
The LFs have been derived in the rest-frame J and Ks bands using 3 z bins
(z_mean= 0.5, 1, 1.5) and compared to the local near-IR LF. The faint-end of
the LFs is consistent with the local estimates, with no evidence for a change
either in the slope or normalization up to z<1.3. Viceversa, the density of
luminous galaxies (M_Ks-5logh_70<-25.5) is higher than locally at all z and
relatively constant or mildly increasing with z within our sample. The data are
consistent with a mild luminosity evolution both in the J and Ks-band up to
z=1.5 (DeltaM_J=-0.69+-0.12 and DeltaM_K=-0.54+-0.12 at z=1). Moreover, we find
that red and early-type galaxies dominate the bright-end of the LF, and that
their number density shows at most a small decrease (<30%) up to z=1, thus
suggesting that massive elliptical galaxies were already in place at z=1 and
they should have formed their stars and assembled their mass at higher z. There
appears to be a correlation of the optical/near-IR colors with near-IR
luminosities, the most luminous/massive galaxies being red/old. We find a slow
evolution with z of the near-IR comoving luminosity density to z=1.5. Finally,
we show that hierarchical models overpredict significantly the density of low
luminosity galaxies at z<=1 and underpredict the density of luminous galaxies
at z>=1, whereas PLE models are more consistent with the data up to z=1.5. The
GIF model (Kaufmann et al. 1999) shows a clear deficiency of red luminous
galaxies at z=1 compared to our observations and predicts a decrease of
luminous galaxies with z not observed in our sample.
