  A connection is proposed between the anomalous thermal transport properties
of amorphous solids and the low-frequency behavior of the Eliashberg function.
By means of a model calculation we show that the size and frequency dependence
of the phonon mean-free-path that has been extracted from measurements of the
thermal conductivity in amorphous solids leads to a sizeable linear region in
the Eliashberg function at small frequencies. Quantitative comparison with
recent experiments gives very good agreement.
