Partial CMB maps: bias removal and optimal binning of the angular power
  spectrum
  We present a semi-analytical method to investigate the systematic effects and
statistical uncertainties of the calculated angular power spectrum when
incomplete spherical maps are used. The computed power spectrum suffers in
particular a loss of angular frequency resolution, which can be written as
\delta_l ~ \pi/\gamma_max, where \gamma_max is the effective maximum extent of
the partial spherical maps. We propose a correction algorithm to reduce
systematic effects on the estimated C_l, as obtained from the partial map
projection on the spherical harmonic Ylm(l,m) basis. We have derived near
optimal bands and weighting functions in l-space for power spectrum calculation
using small maps, and a correction algorithm for partially masked spherical
maps that contain information on the angular correlations on all scales.
