  We consider the time-continuous doubly-dispersive channel with additive
Gaussian noise and establish a capacity formula for the case where the channel
correlation operator is represented by a symbol which is periodic in time and
fulfills some further integrability and smoothness conditions. The key to this
result is a new Szeg\"o formula for certain pseudo-differential operators. The
formula justifies the water-filling principle along time and frequency in terms
of the time--continuous time-varying transfer function (the symbol).
