  We evaluate the dynamic structure factor $S(q,\omega)$ of a one-dimensional
quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland
model). For a fixed small $q$, the structure factor differs from zero in a
finite interval of frequencies of the width $\delta\omega\propto q^2/m$. At the
borders of this interval $S(q,\omega)$ exhibits power-law singularities with
exponents depending only on the interaction strength. The singularities are
similar in origin to the well-known Fermi-edge singularity in the X-ray
absorption spectra of metals.
