  In this investigation, we leverage the combination of Dark Energy
Spectroscopic Instrument Legacy imaging Surveys Data Release 9 (DESI LS DR9),
Survey Validation 3 (SV3), and Year 1 (Y1) data sets to estimate the
conditional luminosity and stellar mass functions (CLFs & CSMFs) of galaxies
across various halo mass bins and redshift ranges. To support our analysis, we
utilize a realistic DESI Mock Galaxy Redshift Survey (MGRS) generated from a
high-resolution Jiutian simulation. An extended halo-based group finder is
applied to both MGRS catalogs and DESI observation. By comparing the r and
z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived
using both photometric and spectroscopic data, we quantified the impact of
photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in
the low redshift bin at low luminosity/mass end. By conducting prior
evaluations of the group finder using MGRS, we successfully obtain a set of CLF
and CSMF measurements from observational data. We find that at low redshift the
faint end slopes of CLFs and CSMFs below $10^{9}h^{-2}L_{\odot}$ (or
$h^{-2}M_{\odot}$) evince a compelling concordance with the subhalo mass
functions. After correcting the cosmic variance effect of our local Universe
following arXiv:1809.00523, the faint end slopes of the LFs/SMFs turn out to be
also in good agreement with the slope of the halo mass function.
