  We present a calculation of the spectral functions and the associated rf
response of ultracold fermionic atoms near a Feshbach resonance. The single
particle spectra are peaked at energies that can be modeled by a modified BCS
dispersion. However, even at very low temperatures their width is comparable to
their energy, except for a small region around the dispersion minimum. The
structure of the excitation spectrum of the unitary gas at infinite scattering
length agrees with recent momentum-resolved rf spectra near the critical
temperature. A detailed comparison is made with momentum integrated, locally
resolved rf spectra of the unitary gas at arbitrary temperatures and shows very
good agreement between theory and experiment. The pair size defined from the
width of these spectra is found to coincide with that obtained from the leading
gradient corrections to the effective field theory of the superfluid.
