Luminosity functions beyond the spectroscopic limit -: I.: Method and near-infrared LFs in the HDF-N and HDF-S

We have developed a Monte Carlo method to compute the luminosity function of galaxies, based on photometric redshifts, which takes into account the non-Gaussianity of the probability functions, and the presence of degenerate solutions in redshift. In this paper we describe the method and the mock tests performed to check its reliability. The NIR luminosity functions and the redshift distributions are determined for near infrared subsamples on the HDF-N and HDF-S. The results on the evolution of the NIR LF, the stellar mass function, and the luminosity density, are presented and discussed in view of the implications for the galaxy formation models. The main results are the lack of substantial evolution of the bright end of the NIR LF and the absence of decline of the luminosity density up to a redshift z similar to 2, implying that most of the stellar population in massive galaxies was already in place at such redshift.