  We present the results of spectroscopic studies with the LRIS spectrograph on
Keck of two of the Hawaii deep survey fields. The 393 objects observed cover an
area of 26.2 square arcmin and constitute a nearly complete sample down to K =
20, I = 23, and B = 24.5. The rest-frame K-band luminosity function and its
evolution with redshift are described. Comparisons are made with other
optically selected (B and I) samples in the literature, and the corresponding
rest-frame B-band luminosity function evolution is presented. The B-band counts
near B = 24 are shown to be a mixture of normal galaxies at modest redshifts
and galaxies undergoing rapid star formation, which have a wide range of masses
and which are spread over the redshift interval from z = 0.2 to beyond z = 1.7.
The luminosity functions, number counts, and color distributions at optical and
IR wavelengths are discussed in terms of a consistent picture of the
star-forming history of the galaxy sample. [OII] emission-line diagnostics or
rest-frame ultra-violet--infrared color information are used in combination
with rest-frame absolute K magnitudes to construct a ``fundamental plane'' in
which the evolution of the global star-formation rate with redshift can be
shown, and we find that the maximum rest-frame K luminosity of galaxies
undergoing rapid star formation has been declining smoothly with decreasing
redshift from a value near L* at z > 1. This smooth decrease in the
characteristic luminosity of galaxies dominated by star formation can
simultaneously account for the high B-band galaxy counts at faint magnitudes
and the redshift distribution at z < 1 in both the B- and K-selected samples.
Finally, the overall K-band light density evolution is discussed as a tracer of
the baryonic mass in stars and compared with the rate of star formation.

Astrophysics