The dielectric function of a cerium oxide nanopowder has been investigated by infrared spectroscopy. The use of Bergman's spectral representation and a semi-quantum dielectric function model allows an accurate retrieval of the main features of the lattice dynamics of this nanocompound. Due to the absence of significant lattice strain or vacancy concentration, the observed differences between the dielectric functions of the nanopowder and a single crystal can be explained mainly by the phenomenon of phonon confinement. The results are validated by comparison to literature data and additional spectroscopic techniques, as well as by direct measurements of powder filling factors.