  We implemented a novel technique to perform the collective spectral analysis
of sets of multiple gamma-ray point sources using the data collected by the
Large Area Telescope onboard the Fermi satellite. The energy spectra of the
sources are reconstructed starting from the photon counts and without assuming
any spectral model for both the sources and the background. In case of faint
sources, upper limits on their fluxes are evaluated with a Bayesian approach.
This analysis technique is very useful when several sources with similar
spectral features are studied, such as sources of gamma rays from annihilation
of dark matter particles. We present the results obtained by applying this
analysis to a sample of dwarf spheroidal galaxies and to the Milky Way dark
matter halo. The analysis of dwarf spheroidal galaxies yields upper limits on
the product of the dark matter pair annihilation cross section and the relative
velocity of annihilating particles that are well below those predicted by the
canonical thermal relic scenario in a mass range from a few GeV to a few tens
of GeV for some annihilation channels.
