This thesis presents the analysis of spectroscopic and photometric data on faint galaxiesin an 8-arcmin diameter region centered on the Hubble Deep Field. Source detection and photometry is performed in the Un, G, R and Ks-band images to createcatalogs complete to Un = 25, G = 26, R = 25.5 and Ks = 20 mag. Number counts and color distributions are consistent with those found in other, similar imagingsurveys. Keck Telescope spectroscopy exists for 483 sources in the sample.
The rest-frame equivalent widths of the [O II] 3727 Å emission line are measuredas a function of galaxy flux, color and redshift. The probability that a source ofa given flux, color and redshift has its [O II] line detected is estimated. [O II] lineluminosity functions and integrated [O II] line luminosity densities are computed;they show strong evolution, implying a much higher star formation rate density at redshiftsz > 0.6 than locally.
The spectroscopic survey is incomplete; not all selected sources have been observedspectroscopically, and not all observed sources have redshifts. Four methods forestimating the luminosity function in an incomplete survey are developed, three basedon the maximum-likelihood method. Simulated catalogs which accurately reproducethe redshift structure and redshift-incompleteness found in real redshift surveys arecreated and used to test the methods for bias. All methods are biased for "steep"(i.e., dwarf-rich) luminosity functions.
The B-band luminosity function for the R-selected sample is computed using anestimate of the probability that a source is assigned a redshift given that it has beenobserved spectroscopically, based on the [O II] detection probability. The luminosityfunction is flat (constant number per log luminosity) and consistent with localdeterminations except for a higher overall normalization. No evidence is found fordependence of the luminosity function on redshift or environment, but the blue galaxyluminosity function is more dwarf-rich than the red.
It is argued that, taken together, the observations support the existence of a dwarf-dominated, strongly star forming galaxy population in the past which merged into (or otherwise became physically associated with) the luminous galaxies observed locally.
