In radio/microwave observations, I understand the beamsize is the response of the telescope to a point source - effectively, the telescope's resolution.
Now, the Planck satellite (par exemple) combines different frequency channels in a variance-weighted map. These different channels in general will have different sensitivities, and different beamsizes.
Suppose you coadd two (or any number really) of these channels. What will be the effective resolution of the resulting map? For instance, suppose we take channel 1 with a 5 arcminute beamsize (FWHM), and channel 2 with a 12 arcminute beamsize (and let's suppose they have the same sensitivity). What will be the resolution of the inverse-variance weighted map? How will this change if the sensitivities differ?