We present the results of numerical experiments designed to evaluate the
usefulness of near-infrared luminosity functions for constraining the Initial
Mass Function (IMF) of young stellar populations. From this numerical modeling,
we find that the luminosity function of a young stellar population is
considerably more sensitive to variations in the underlying initial mass
function than to either variations in the star forming history or assumed
pre-main-sequence (PMS) mass-to-luminosity relation. To illustrate the
potential effectiveness of using the KLF of a young cluster to constrain its
IMF, we model the observed K band luminosity function of the nearby Trapezium
cluster. Our derived mass function for the Trapezium spans two orders of
magnitude in stellar mass (5 Msun to 0.02 Msun), has a peak near the hydrogen
burning limit, and has an IMF for Brown Dwarfs which steadily decreases with
decreasing mass.Comment: To appear in ApJ (1 April 2000). 37 pages including 11 figures, AAS:
ver 5.