  We consider the Cauchy problem for the weakly dissipative wave equation $$
\bx v+\frac\mu{1+t}v_t=0, \qquad x\in\R^n,\quad t\ge 0, $$ parameterized by
$\mu>0$, and prove a representation theorem for its solution using the theory
of special functions.
  This representation is used to obtain $L_p$--$L_q$ estimates for the solution
and for the energy operator corresponding to this Cauchy problem.
  Especially for the $L_2$ energy estimate we determine the part of the phase
sp which is responsible for the decay rate. It will be shown that the situation
d strongly on the value of $\mu$ and that $\mu=2$ is critical.
