  The f-electron spectral function of the Falicov-Kimball model is calculated
within the dynamical mean-field theory using the numerical renormalization
group method as the impurity solver. Both the Bethe lattice and the hypercubic
lattice are considered at half filling. For small U we obtain a single-peaked
f-electron spectral function, which --for zero temperature-- exhibits an
algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \to 0$. The
characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation
U. This X-ray singularity cannot be observed when using alternative
(Keldysh-based) many-body approaches. With increasing U, $\alpha$ decreases and
vanishes for sufficiently large U when the f-electron spectral function
develops a gap and a two-peak structure (metal-insulator transition).
