  In 1,2 or 3 dimensions a scalar wave excited by a non-negative source in a
viscoelastic medium with a non-negative relaxation spectrum or a Newtonian
response or both combined inherits the sign of the source. The key assumption
is a constitutive relation which involves the sum of a Newtonian viscosity term
and a memory term with a completely monotone relaxation kernel. In
higher-dimensional spaces this result holds for sufficiently regular sources.
Two positivity results for vector-valued wave fields including isotropic
viscoelasticity are also obtained. Positivity is also shown to hold under
weakened hypotheses.
