  The equations of the mode-coupling theory (MCT) for ideal liquid-glass
transitions are used for a discussion of the evolution of the
density-fluctuation spectra of glass-forming systems for frequencies within the
dynamical window between the band of high-frequency motion and the band of
low-frequency-structural-relaxation processes. It is shown that the strong
interaction between density fluctuations with microscopic wave length and the
arrested glass structure causes an anomalous-oscillation peak, which exhibits
the properties of the so-called boson peak. It produces an elastic modulus
which governs the hybridization of density fluctuations of mesoscopic wave
length with the boson-peak oscillations. This leads to the existence of
high-frequency sound with properties as found by X-ray-scattering spectroscopy
of glasses and glassy liquids. The results of the theory are demonstrated for a
model of the hard-sphere system. It is also derived that certain schematic MCT
models, whose spectra for the stiff-glass states can be expressed by elementary
formulas, provide reasonable approximations for the solutions of the general
MCT equations.
